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 Applied and Numerical Harmonic Analysis

Matthew Hirn
Shidong Li
Kasso A. Okoudjou
Sandra Saliani
Özgür Yilmaz
Editors

Excursions
in Harmonic
Analysis,
Volume 6
In Honor of John Benedetto’s
80th Birthday
Applied and Numerical Harmonic Analysis

Series Editor
John J. Benedetto
University of Maryland
College Park, MD, USA

Advisory Editors

Akram Aldroubi Gitta Kutyniok

Vanderbilt University Ludwig Maximilian University
Nashville, TN, USA Munich, Germany

Douglas Cochran Mauro Maggioni

Arizona State University Johns Hopkins University
Phoenix, AZ, USA Baltimore, MD, USA

Hans G. Feichtinger Zuowei Shen

University of Vienna National University of Singapore
Vienna, Austria Singapore, Singapore

Christopher Heil Thomas Strohmer

Georgia Institute of Technology University of California
Atlanta, GA, USA Davis, CA, USA

Stéphane Jaffard Yang Wang

University of Paris XII Hong Kong University of
Paris, France Science & Technology
Kowloon, Hong Kong
Jelena Kovačević
New York University
New York, NY, USA

More information about this series at http://www.springer.com/series/4968

Matthew Hirn • Shidong Li • Kasso A. Okoudjou
Sandra Saliani • Özgür Yilmaz
Editors

Excursions in Harmonic
Analysis, Volume 6
In Honor of John Benedetto’s 80th Birthday
Editors
Matthew Hirn Shidong Li
Department of Computational Mathematics, Department of Mathematics
Science & Engineering San Francisco State University
Michigan State University San Francisco, CA, USA
East Lansing, MI, USA
Sandra Saliani
Kasso A. Okoudjou Department of Mathematics
Department of Mathematics Computer Science and Economics
Tufts University University of Basilicata
Medford, MA, USA Potenza, PZ, Italy

Özgür Yilmaz
Department of Mathematics
University of British Columbia
Vancouver, BC, Canada

ISSN 2296-5009 ISSN 2296-5017 (electronic)

Applied and Numerical Harmonic Analysis
ISBN 978-3-030-69636-8 ISBN 978-3-030-69637-5 (eBook)
https://doi.org/10.1007/978-3-030-69637-5

Mathematics Subject Classification: 43-XX

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland
AG 2021
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse
of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
transmission or information storage and retrieval, electronic adaptation, computer software, or by similar
or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.

This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered
company Springer Nature Switzerland AG.
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to Cathy
ANHA Series Preface

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to
provide the engineering, mathematical, and scientific communities with significant
developments in harmonic analysis, ranging from abstract harmonic analysis to
basic applications. The title of the series reflects the importance of applications
and numerical implementation, but richness and relevance of applications and
implementation depend fundamentally on the structure and depth of theoretical
underpinnings. Thus, from our point of view, the interleaving of theory and
applications and their creative symbiotic evolution is axiomatic.
Harmonic analysis is a wellspring of ideas and applicability that has flourished,
developed, and deepened over time within many disciplines and by means of
creative cross-fertilization with diverse areas. The intricate and fundamental
relationship between harmonic analysis and fields such as signal processing, partial
differential equations (PDEs), and image processing is reflected in our state-of-the-
art ANHA series.
Our vision of modern harmonic analysis includes mathematical areas such as
wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis,
and fractal geometry, as well as the diverse topics that impinge on them.
For example, wavelet theory can be considered an appropriate tool to deal with
some basic problems in digital signal processing, speech and image processing,
geophysics, pattern recognition, biomedical engineering, and turbulence. These
areas implement the latest technology from sampling methods on surfaces to fast
algorithms and computer vision methods. The underlying mathematics of wavelet
theory depends not only on classical Fourier analysis, but also on ideas from abstract
harmonic analysis, including von Neumann algebras and the affine group. This leads
to a study of the Heisenberg group and its relationship to Gabor systems, and of the
metaplectic group for a meaningful interaction of signal decomposition methods.
The unifying influence of wavelet theory in the aforementioned topics illustrates the
justification for providing a means for centralizing and disseminating information
from the broader, but still focused, area of harmonic analysis. This will be a key role
of ANHA. We intend to publish with the scope and interaction that such a host of
issues demands.

vii
viii ANHA Series Preface

Along with our commitment to publish mathematically significant works at the

frontiers of harmonic analysis, we have a comparably strong commitment to publish
major advances in the following applicable topics in which harmonic analysis plays
a substantial role:

Antenna theory Prediction theory

Biomedical signal processing Radar applications
Digital signal processing Sampling theory
Fast algorithms Spectral estimation
Gabor theory and applications Speech processing
Image processing Time-frequency and
Numerical partial differential equations Time-scale analysis
Wavelet theory

The above point of view for the ANHA book series is inspired by the history of
Fourier analysis itself, whose tentacles reach into so many fields.
In the last two centuries Fourier analysis has had a major impact on the
development of mathematics, on the understanding of many engineering and
scientific phenomena, and on the solution of some of the most important problems
in mathematics and the sciences. Historically, Fourier series were developed in
the analysis of some of the classical PDEs of mathematical physics; these series
were used to solve such equations. In order to understand Fourier series and the
kinds of solutions they could represent, some of the most basic notions of analysis
were defined, e.g., the concept of “function." Since the coefficients of Fourier
series are integrals, it is no surprise that Riemann integrals were conceived to deal
with uniqueness properties of trigonometric series. Cantor’s set theory was also
developed because of such uniqueness questions.
A basic problem in Fourier analysis is to show how complicated phenomena,
such as sound waves, can be described in terms of elementary harmonics. There are
two aspects of this problem: first, to find, or even define properly, the harmonics or
spectrum of a given phenomenon, e.g., the spectroscopy problem in optics; second,
to determine which phenomena can be constructed from given classes of harmonics,
as done, for example, by the mechanical synthesizers in tidal analysis.
Fourier analysis is also the natural setting for many other problems in engineer-
ing, mathematics, and the sciences. For example, Wiener’s Tauberian theorem in
Fourier analysis not only characterizes the behavior of the prime numbers, but also
provides the proper notion of spectrum for phenomena such as white light; this
latter process leads to the Fourier analysis associated with correlation functions in
filtering and prediction problems, and these problems, in turn, deal naturally with
Hardy spaces in the theory of complex variables.
Nowadays, some of the theory of PDEs has given way to the study of Fourier
integral operators. Problems in antenna theory are studied in terms of unimodular
trigonometric polynomials. Applications of Fourier analysis abound in signal
ANHA Series Preface ix

processing, whether with the fast Fourier transform (FFT), or filter design, or the
adaptive modeling inherent in time-frequency-scale methods such as wavelet theory.
The coherent states of mathematical physics are translated and modulated Fourier
transforms, and these are used, in conjunction with the uncertainty principle, for
dealing with signal reconstruction in communications theory. We are back to the
raison d’être of the ANHA series!

University of Maryland John J. Benedetto

College Park Series Editor
Foreword

John Benedetto was the first doctoral thesis student I supervised. It is sort of
inadvisable to start out with a graduate student like that: it may saddle you, going
forward, with unrealistically high expectations.
But, we were a good pair: John bright-eyed and brash in his twenties, just getting
into the thesis student’s role, and me bright-eyed and brash in my thirties, just
getting into the thesis adviser’s role. Actually, John was intent not only on writing a
thesis on analysis and Banach spaces with me but also on learning all about Thomist
philosophy from the eminent French philosopher Étienne Gilson on the other side of
the Toronto campus. I did not know about this double ambition of his at the time—
John reminisced about it to me only some years later, having found meanwhile
that it was a bit much to juggle the two specialties at once. If I had known I was
dealing with a mathematician cum medieval philosopher, actually, it would have
made John seem even more akin, because I at the same stage of my education had
set out not only to become a mathematician in the image of George Mackey and
Garrett Birkhoff but at the same time to become a composer in the image of Irving
Fine. And, I would not have been let down when John gave up his philosophical
moonlighting, for I had had to give up my concentration on music in the same way.
So, John was declared Doctor of Philosophy and launched on his professional
career with my blessing and that of the University of Toronto. I applauded his
service in New York, Maryland, Pisa, and elsewhere. It may seem that our research
emphases diverged a bit, but it does not feel to me that we got out of touch. In
particular, we both welcomed the rise of wavelet theory with enthusiasm and without
needing to consult each other. But, I remained mostly a spectator, while John threw
himself into the amazing development of applied Fourier analysis. He became one
of the leaders in forming the field and in making it known to a wider public, and he
leads a large phalanx of creative Fourier analysts in the next generation. I have been
duly appreciative of the achievements of the Norbert Wiener Center, though I have
viewed them mostly from afar.

xi
xii Foreword

One has no right to take pride in the work of one’s students and grandstudents,
but I confess to feeling that pride in this case, however, unjustified. May they carry
on whatever in my own life deserves to be carried on.

Toronto, ON, Canada Chandler Davis

May 2020
Preface

“John J. Benedetto has had a profound influence not only on the direction of
harmonic analysis and its applications, but also on the entire community of people
involved in the field.” This statement can be found in the preface of the volume
celebrating John’s 60th birthday and holds true even more so today. During the
20 years that follows, the world has witnessed that the breadth and depth of
John’s influence continue to expand. Besides his enormously impactful scientific
research contributions, John’s influence also lies in, for instance, advising 61
Ph.D. students (so far) and nurturing many other junior scholars; founding the
Journal of Fourier Analysis and Applications (JFAA), and the book series of
Applied and Numerical Harmonic Analysis (ANHA); establishing the renowned
Norbert Winner Center, and fostering a wide range of highly relevant health and
scientific research. All in all, John’s most profound influence lies in his building
of a worldwide community of scholars in harmonic analysis and its applications.
Advancing beautiful mathematical ideas and applications is an underlying theme of
John’s illustrious career and is continuing in the latest forum of the annual February
Fourier Talks (FFT). A full account of John’s influence on the field of harmonic
analysis would require volumes.
In honor of John’s 80th birthday, this book is another assemblage of community’s
appreciation to John’s deep impact on the field of harmonic analysis and applications
and to the scientific community. Needless to say, the original articles collected in this
volume are all highly relevant and written by prominent, well-respected scholars in
the field. This volume covers an invited chapter and the following five parts:
1. John Benedetto’s Mathematical Work,
2. Harmonic Analysis,
3. Wavelets and Frames,
4. Sampling and Signal Processing,
5. Compressed Sensing and Optimizations.
As such, this book shall be once again an excellent reference and resource
for graduate students and professionals in the field. Contributors of the volume
include A. Abtahi, A. Aldroubi, C. Cabrelli, P.G. Casazza, J. Cahill, D.-C. Chang,

xiii
xiv Preface

E. Cordero, W. Czaja, S.B. Damelin, S. Data, M. Dorfler, N. Dyn, M. de Gosson,

Y. Han, C. Hegde, C. Heil, J.A. Hogan, Y. Hu, R. Johnson, D. Joyner, F. Keinert,
J.D. Lakey, C. Leonard, W. Li, Y. Li, R.D. Martin, F. Marvasti, I. Medri, K.D.
Merrill, D.G. Mixon, U. Molter, F. Nicola, A. Olevskii, M. Pekala, I.Z. Pesenson,
A. Petrosyan, D.L. Ragozin, T. Strohmer, J. Stueck, T.T. Tran, A. Ulanovskii, E.S.
Weber, M. Werman, T. Wertz, X. Wu, S. Zheng, and X. Zhuang.
To close, we would like to thank Radu V. Balan, Wojciech Czaja, Luke Evans,
Alfredo Nava-Tudela, and Kasso Okoudjou, for organizing the conference celebrat-
ing John’s birthday, and Jean-Pierre Gabardo, Christopher Heil, Emily King, Götz
Pfander, and David Walnut for putting together an outstanding scientific program.
We also acknowledge the financial support of the Institute for Mathematics and its
Applications and the Department of Mathematics at the University of Maryland.

East Lansing, MI, USA Matthew Hirn

San Francisco, CA, USA Shidong Li
Medford, MA, USA Kasso A. Okoudjou
Potenza, PZ, Italy Sandra Saliani
Vancouver, BC, Canada Özgür Yilmaz
November 2020
Contents

Part I Introduction
John Benedetto’s Mathematical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
David Joyner

Part II Harmonic Analysis

Absolute Continuity and the Banach–Zaretsky Theorem . . . . . . . . . . . . . . . . . . . 27
Christopher Heil
Spectral Synthesis and H 1 (R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Raymond Johnson
Universal Upper Bound on the Blowup Rate of Nonlinear
Schrödinger Equation with Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Yi Hu, Christopher Leonard, and Shijun Zheng
Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators . . . . . . 77
Thomas Strohmer and Timothy Wertz
Spatio–Spectral Limiting on Redundant Cubes: A Case Study . . . . . . . . . . . . 97
Jeffrey A. Hogan and Joseph D. Lakey

Part III Wavelets and Frames

A Notion of Optimal Packings of Subspaces with Mixed-Rank
and Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Peter G. Casazza, Joshua Stueck, and Tin T. Tran
Construction of Frames Using Calderón–Zygmund Operator Theory . . . . 145
Der-Chen Chang, Yongsheng Han, and Xinfeng Wu
Equiangular Frames and Their Duals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Somantika Datta

xv
xvi Contents

Wavelet Sets for Crystallographic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Kathy D. Merrill
Discrete Translates in Function Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Alexander Olevskii and Alexander Ulanovskii

Part IV Sampling and Signal Processing

Local-to-Global Frames and Applications to the Dynamical
Sampling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Akram Aldroubi, Carlos Cabrelli, Ursula Molter, and Armenak Petrosyan
Signal Analysis Using Born–Jordan-Type Distributions . . . . . . . . . . . . . . . . . . . . 221
Elena Cordero, Maurice de Gosson, Monika Dörfler, and Fabio Nicola
Sampling by Averages and Average Splines on Dirichlet Spaces
and on Combinatorial Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Isaac Z. Pesenson
Dynamical Sampling: A View from Control Theory . . . . . . . . . . . . . . . . . . . . . . . . . 269
Rocío Díaz Martín, Ivan Medri, and Ursula Molter
Linear Multiscale Transforms Based on Even-Reversible
Subdivision Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Nira Dyn and Xiaosheng Zhuang

Part V Compressed Sensing and Optimization

Sparsity-Based MIMO Radars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Azra Abtahi and Farokh Marvasti
Robust Width: A Characterization of Uniformly Stable and
Robust Compressed Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Jameson Cahill and Dustin G. Mixon
On Min-Max Affine Approximants of Convex or Concave
Real-Valued Functions from Rk , Chebyshev Equioscillation
and Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
Steven B. Damelin, David L. Ragozin and Michael Werman
A Kaczmarz Algorithm for Solving Tree Based Distributed
Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Chinmay Hegde, Fritz Keinert, and Eric S. Weber
Maximal Function Pooling with Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Wojciech Czaja, Weilin Li, Yiran Li, and Mike Pekala

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Contributors

Azra Abtahi Advanced Communications Research Institute (ACRI), Electrical

Engineering Department, Sharif University of Technology, Tehran, Iran
Akram Aldroubi Department of Mathematics, Vanderbilt University, Nashville,
TN, USA
Carlos Cabrelli Departamento de Matemática, FCEyN, UBA and IMAS CON-
ICET, Buenos Aires, Argentina
Jameson Cahill University of North Carolina Wilmington, Wilmington, NC, USA
Peter G. Casazza Department of Mathematics, University of Missouri, Columbia,
MO, USA
Der-Chen Chang Department of Mathematics and Statistics, Georgetown Univer-
sity, Washington, DC, USA
Graduate Institute of Business Administration, College of Management, Fu Jen
Catholic University, New Taipei City, Taiwan
Elena Cordero Università di Torino, Dipartimento di Matematica, Torino, Italy
Wojciech Czaja Norbert Wiener Center, Department of Mathematics, University
of Maryland College Park, College Park, MD, USA
Steven B. Damelin Department of Mathematics, University of Michigan, Ann
Arbor, MI, USA
Somantika Datta Department of Mathematics, University of Idaho, Moscow, ID,
USA
Maurice de Gosson University of Vienna, Faculty of Mathematics, Wien, Austria
Rocío Díaz Martín IAM – CONICET, CABA, Argentina
Universidad Nacional de Córdoba, Córdoba, Argentina
Monika Dörfler University of Vienna, Faculty of Mathematics, Wien, Austria

xvii
xviii Contributors

Nira Dyn School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel

Yongsheng Han Department of Mathematics and Statistics, Auburn University,
Auburn, AL, USA
Chinmay Hegde Electrical and Computer Engineering, Iowa State University,
Ames, IA, USA
Electrical and Computer Engineering, New York University, New York, NY, USA
Christopher Heil School of Mathematics, Georgia Tech, Atlanta, GA, USA
Jeffrey A. Hogan School of Mathematical and Physical Sciences, University of
Newcastle, Callaghan, NSW, Australia
Yi Hu Department of Mathematical Sciences, Georgia Southern University, States-
boro, GA, USA
Raymond Johnson University of Maryland, College Park, MD, USA
David Joyner Department of Mathematics, U.S. Naval Academy (Retired),
Annapolis, MD, USA
Fritz Keinert Department of Mathematics, Iowa State University, Ames, IA, USA
Joseph D. Lakey New Mexico State University, Las Cruces, NM, USA
Christopher Leonard Department of Mathematics, North Carolina State Univer-
sity, Raleigh, NC, USA
Weilin Li Courant Institute of Mathematical Sciences, New York University,
New York, NY, USA
Yiran Li Norbert Wiener Center, Department of Mathematics, University of
Maryland College Park, College Park, MD, USA
Farokh Marvasti Advanced Communications Research Institute (ACRI), Electri-
cal Engineering Department, Sharif University of Technology, Tehran, Iran
Ivan Medri Department of Mathematics, Vanderbilt University, Nashville, TN,
USA
Kathy D. Merrill Department of Mathematics, Colorado College, Colorado
Springs, CO, USA
Dustin G. Mixon The Ohio State University, Columbus, OH, USA
Ursula Molter Dto. de Matemática, FCEyN, Universidad de Buenos Aires,
Buenos Aires, Argentina
Fabio Nicola Politecnico di Torino, Dipartimento di Scienze Matematiche, Torino,
Italy
Alexander Olevskii Tel Aviv University, Tel Aviv, Israel
Contributors xix

Mike Pekala Norbert Wiener Center, Department of Mathematics, University of

Maryland College Park, College Park, MD, USA
Isaac Z. Pesenson Department of Mathematics, Temple University, Philadelphia,
PA, USA
Armenak Petrosyan Computational and Applied Mathematics Group, Oak Ridge
National Laboratory, Oak Ridge, TN, USA
David L. Ragozin Department of Mathematics, University of Washington, Seattle,
WA, USA
Thomas Strohmer University of California, Davis, CA, USA
Joshua Stueck Department of Mathematics, University of Missouri, Columbia,
MO, USA
Tin T. Tran Department of Mathematics, University of Missouri, Columbia, MO,
USA
Alexander Ulanovskii Stavanger University, Stavanger, Norway
Eric S. Weber Department of Mathematics, Iowa State University, Ames, IA, USA
Michael Werman Department of Computer Science, The Hebrew University,
Jerusalem, Israel
Timothy Wertz Yale-NUS College, Singapore, Singapore
Xinfeng Wu Department of Mathematics, China University of Mining and Tech-
nology, Beijing, P.R. China
Shijun Zheng Department of Mathematical Sciences, Georgia Southern Univer-
sity, Statesboro, GA, USA
Xiaosheng Zhuang Department of Mathematics, City University of Hong Kong,
Kowloon, Hong Kong
Acronyms

AC Absolutely continuous
ACO Approximately controllable
AOB Approximately observable
ART Algebraic Reconstruction Technique: a method of image recon-
struction in computerized tomography
BEC Bose–Einstein condensation
BIBD Balanced incomplete block design
BJ Born–Jordan distribution
BJDn Born–Jordan distribution of order n
BV Bounded variation
CNN Convolutional neural network
CPU Central processing unit
CS Compressive sensing
CSC Convolutional sparse coding
DCP Deep coding problem
DCPP Deep coding problem with pooling
DOA/DOD Directions of arrival/departure
DS Dynamical sampling
ECO Exactly controllable
EF Equiangular frame
ENR Ratio of total transmitted energy to the noise energy
EOB Exactly observable
ETF Equiangular tight frame
ETFF Equiangular tight fusion frame
FFT February Fourier Talks
FTC Fundamental Theorem of Calculus
GFT Graph Fourier transform
IBM International Business Machines
JB John Benedetto
Lip Lipschitz continuous
LMS License in Mediaeval Studies

xxi
xxii Acronyms

MIMO Radar Multiple-input multiple-output radar

MIT Massachusetts Institute of Technology
ML Maximum likelihood
MRA Multiresolution analysis
MTER Multiscale transform based on an even-reversible subdivision
MUBs Mutually unbiased bases
NLS Nonlinear Schrödinger equation
NP-hard Nondeterministic polynomial-time hard
NWC Norbert Wiener Center for Harmonic Analysis and Applications
NYU New York University
PDE Partial differential equation
RCA Radio Corporation of America
RGS Reynolds Gauss–Seidel method
ROC Receiver operating characteristic
RNLS Rotational nonlinear Schrödinger equation
RS Random sampling
SNR Signal-to-noise ratio
SOR Successive over-relaxation method
SPIE Society of Photographic Instrumentation Engineers
SSL Spatio-spectral limiting
SSN Spectral neutral neighbor
SVM Support vector machine
TA Teaching assistant
UMCP University of Maryland at College Park
 Part I
Introduction

The first part of this volume serves as its introduction and contains a single chapter
in which D. Joyner summarizes the mathematical work of John, including an
exhaustive list of his students and publications.
John Benedetto’s Mathematical Work

David Joyner

Abstract John Joseph Benedetto (JB) has been at the University of Maryland,
College Park, since 1965. In this chapter, I will submit data that attests to JB’s (a)
large number of PhD students, (b) large number of papers (As a linear regression
computation shows, the number of PhD students (per year) he advises and the
number of papers (published per year) are both increasing, on average. See below.),
and (c) remarkable outreach into the business sector, inviting cooperation between
industry and his group of UMCP mathematicians that became the Norbert Wiener
Center.

1 Brief Biography

On June 17, 1933, Vienna DiTonno married John (“Zip”) Benedetto in Wakefield,
Mass., the working class town just north of Boston where they were born and raised.
Zip and Vienna were children of the depression and never got past 8th grade in
school. Their only child, JB was born there six years later, on July 16, 1939.
Zip ran a pool hall in downtown Wakefield. While JB was an excellent student,
in high school he got no further than trigonometry and solid geometry, as they did
not teach calculus at the time. After school, to his mom’s dismay, JB would visit
the pool hall almost daily to help his dad run his business (and to play a little
pool!). Another person who frequented Zip’s pool hall was Robert McCloskey, a
Harvard professor1 and a collegiate billiards champion as an undergraduate. Seeing
JB’s academic talent, McCloskey told Zip2 to encourage JB to apply to Harvard.
However, after JB graduated from Malden Catholic High School in 1956, he applied

1 According to archives of “The Crimson,” McCloskey was appointed Chair of the Government
Department at Harvard in 1958.
2 Sadly, Zip passed away at age 44 in May of 1956, when JB was 16.

D. Joyner ()
Department of Mathematics, U.S. Naval Academy (Retired), Annapolis, MD, USA

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 3

M. Hirn et al. (eds.), Excursions in Harmonic Analysis, Volume 6, Applied and
Numerical Harmonic Analysis, https://doi.org/10.1007/978-3-030-69637-5_1
4 D. Joyner

(and was accepted) to Boston College instead of Harvard. At Boston College, he had
inspirational teachers for his first- and second-year mathematics courses, convincing
JB to major in mathematics. As a nod perhaps to McCloskey, as a senior, JB applied
to Harvard for graduate school, and nowhere else. Fortunately for mathematics, he
was accepted and, after graduating from Boston College in 1960, began to take
courses from Gleason (real analysis), Widder (Laplace transforms), Mackey, and
Walsh (of Walsh functions fame), among others. His master’s degree was awarded
by Harvard in 1962.
In the fall of 1962, JB left Harvard for the University of Toronto, where he
studied with Chandler Davis,3 who JB did not know of at Harvard. The reason
for this move to Canada is not as simple as it sounds. It has really nothing to
do with the fact that both Walsh and Davis had advisors in the Birkhoff family
(and both on the Harvard faculty). At Boston College and Harvard, JB was very
interested in Thomistic philosophy (the philosophy of Thomas Aquinas), and he
knew the Pontifical Institute of Medieval Studies at St. Michael’s College was a
subset of the University of Toronto. His plan was to get a PhD in mathematics
in 1964 and an LMS from the Pontifical Institute4 along the way. JB even knew
what he wanted to work on for his PhD: the Laplace transform of distributions and
topological vector spaces.5 So, in the summer of 1962, JB is a man who knows
what he wants. However, once JB arrived in Toronto that fall, life had other plans.
First, JB was assigned as a TA to Chandler Davis. That is how they met and started
working together. Second, he started taking classes at the Pontifical Institute, but
after the first philosophy course dropped his plan to get an LMS. In fact, JB was
Chandler Davis’ first PhD student, and they got along very well.6 JB’s PhD degree
was awarded by the University of Toronto a few years later in 1964, and a revised
version of his thesis was published in [1966b] (Fig. 1).
In 1964, after graduating, JB took a tenure-track job at New York University.7
While a graduate student, during the summers JB worked at RCA in Burlington,
MA. However, starting the summer of 1964 and part time during the academic year,
JB worked at IBM Cambridge, instead of RCA. On a whim, JB left NYU for a
tenure-track position at UMCP the following year. Except for visiting positions at
MIT, the Mittag-Leffler Institute, and Scuola Normale Superiore, JB has been at
UMCP since 1965. Once at UMCP, JB continued to consult for industry but, of
course, eventually this work came under the umbrella of the Norbert Wiener Center
(more on that below).

3 From the it’s-a-small-world department, Chandler Davis’ PhD advisor was Garrett Birkhoff, son
of George David Birkhoff, who was Joseph Walsh’s PhD advisor.
4 The LMS, a License in Mediaeval Studies or “Licentiate,” is a kind of post-graduate degree

awarded by The Pontifical Institute of Mediaeval Studies. There is no analogous degree offered
in the United States.
5 Inspired by Widder’s course on the Laplace transform and the reading course with Mackey on

distributions and topological vector space that he took at Harvard.

6 JB has written about his connection with Chandler Davis in [2014a].
7 That year, the Courant Institute moved to its current location, in Weaver Hall.
John Benedetto’s Mathematical Work 5

Fig. 1 JB getting his PhD,

with mom Vienna and
grandpa Mr. DiTonno in 1964

As far as the arc of his career is concerned, JB’s main mathematical inspirations
are:
• Chandler Davis (PhD advisor) (Fig. 2),
• N. Wiener (whom JB never met),
• A. Beurling (whom JB never met),
• A. Gleason, one of his teachers at Harvard.
While JB has told me that many of the ideas he gets for papers are from thinking
about mathematics while on a walk or traveling, I know there is another source: lots
of hand computations. To illustrate this, I will tell a story connected with my PhD
thesis (in 1983, shortly after the publication of my favorite paper of his, [1980a]).
As a graduate student, he assigned me a problem connected with his Mathematische
Annalen 1980 paper. I do not remember the problem, but I remember that after I
solved it, I did not want to take credit for it if he already solved it but just did
not, for whatever reason, add it to his paper. So one day, we had a meeting in his
office about this psychological problem I was having. He said to resolve the matter,
I could read the notes he made while writing the paper. Apparently, for each paper
JB writes, he keeps his notes (or at least, did at the time) in a notebook. So, JB pulls
out this massive notebook (the kind with the extra large rings) full of hand-written
computations. That JB keep such a massive set of detailed notes for each paper was
amazing to me at the time, and still is.
In his career, JB has been a Senior Fulbright-Hays Scholar, a SPIE Wavelet
Pioneer, a Fellow of the American Mathematical Society, and a SIAM Fellow. His
6 D. Joyner

Fig. 2 Chandler Davis and

JB in 1964

paper [1989b] won MITRE’s Best Paper Award, and he was named Distinguished
Scholar-Teacher by the University of Maryland in 1999.
Currently, JB is the Director of the Norbert Wiener Center for Harmonic Analysis
and Applications (NWC), which he founded in 2004. It serves as an interface
between funding agencies and industry with problems that can be solved using
harmonic analysis by mathematicians at the NWC.8 In its 15 years of existence,
the mathematicians at the NWC have brought in over 7 million dollars in grants and
have worked with over 15 industrial partners.9 Besides dollar grants, many of these
industrial partners have also supported numerous student internships. Hundreds
have spoken at or attended the annual NWC conference, the February Fourier Talks,
or FFT. The NWC is also connected with the Journal of Fourier Analysis and its
Applications10 and the Applied and Numerical Harmonic Analysis book series.11
As of summer 2019, JB has directed 58 PhD students (with several more in the
pipeline). As of this writing, JB is in the top 100 of all PhD advisors worldwide.12
JB does not co-author published PhD theses of his PhD students. Nonetheless, he
has over 200 publications, of this writing, and over 80 co-authors (many of which
are his former PhD students, if they do research with JB going beyond their thesis).
What is even more impressive is that none of JB’s academic publications were co-
authored until 1983. At the time of this writing, JB’s most frequent co-author (by
far) is his UMCP colleague, Wojciech Czaja.

8 Currently,JB, Radu Balan, Wojciech Czaja, and Kasso Okoudjou.

9 For example, NIH, AFOSR, Siemens, MITRE, DARPA, ONR, NSF, and many more.
10 For which JB is the Founding Editor-in-Chief.
11 For which JB is the Series Editor.
12 According to the database “Mathematics Genealogy Project.”
John Benedetto’s Mathematical Work 7

2 Coda

In summary, JB’s piercing intellectual curiosity has led to over 200 hundred refereed
publications and about 60 PhD students, so far. Which reminds me of the old joke,
“Great mathematicians never die, they just tend to infinity.”

3 PhD Theses

Here is a list of the 61 (and counting) PhD students that JB has advised.
1. 1971, George Benke, Sidon sets and the growth of Lp norms
2. 1977a, Wan-Chen Hsieh, Topologies for spectral synthesis of the space of
bounded functions
3. 1977b, Fulvio Ricci, Support preserving multiplication of pseudo-measures
4. 1980, Ward Evans,13 Beurling’s spectral analysis and continuous pseudo-
measures
5. 1983, W. David Joyner, The harmonic analysis of Dirichlet series and the
Riemann zeta function
NSF Post-Doc IAS 1984.
6. 1987, Jean-Pierre Gabardo, Spectral gaps and uniqueness problems in Fourier
analysis
Sloan Dissertation Fellowship 1986.
7. 1989, David Walnut, Weyl–Heisenberg wavelet expansions: existence and
stability in weighted spaces
Sloan Dissertation Fellowship 1988
8. 1990a, Christopher Heil, Wiener amalgam spaces in generalized harmonic
analysis and wavelet theory
NSF Post-Doc MIT 1990
9. 1990b, Rodney Kerby, Correlation function and the Wiener–Wintner theorem
in higher dimensions
10. 1990c, George Yang, Applications of Wiener–Tauberian theorem to a filtering
problem and convolution equations
11. 1991a, William Heller, Frames of exponentials and applications
12. 1991b, Joseph Lakey, Weighted norm inequalities for the Fourier transform
13. 1992, Erica Bernstein, Generalized Riesz products and pyramidal schemes
14. 1993a, Shidong Li, The theory of frame multiresolution analysis and filter
design
15. 1993b, Sandra Saliani, Nonlinear wavelet packets
16. 1993c, Anthony Teolis, Discrete signal representation
17. 1994, Georg Zimmermann, Projective multiresolution analysis and generalized
sampling

13 Now named Celia Evans.

8 D. Joyner

18. 1998a, Melissa Harrison, Frames and irregular sampling from a computational
perspective
19. 1998b, Hui-Chuan Wu, Multidimensional irregular sampling in terms of frames
20. 1999a, Manuel Leon, Minimally supported frequency wavelets
21. 1999b, Götz Pfander, Periodic wavelet transforms and periodicity detection
22. 1999c, Oliver Treiber, Affine data representations and filter banks
23. 2000, Sherry Scott, Spectral analysis of fractal noise in terms of Wiener’s
generalized harmonic analysis and wavelet theory
24. 2001a, Matthew Fickus, Finite normalized tight frames and spherical equidis-
tribution
25. 2001b, Ioannis Konstantinidis, The characterization of multiscale generalized
Riesz product measures
26. 2002a, Anwar A. Saleh, A finite dimensional model for the inverse frame
operator
27. 2002b, Jeffrey Sieracki, Greedy adaptive discrimination: Signal component
analysis by simultaneous matching pursuit with application to ECoG signature
detection
28. 2002c, Songkiat Sumetkijakan, A fractal set constructed from a class of wavelet
sets
29. 2003a, Alexander M. Powell, The uncertainty principle in harmonic analysis
and Bourgain’s theorem
Dissertation Fellowship 2000
30. 2003b, Shijun Zheng, Besov spaces for the Schrödinger operator with barrier
potential
Dissertation Fellowship 2000
31. 2004, Joseph Kolesar, – modulation and correlation criteria for the con-
struction of finite frames arising in communication theory
32. 2005a, Andrew Kebo, Quantum detection and finite frames
33. 2005b, Juan Romero, Generalized multiresolution analysis: construction and
measure-theoretic characterization
34. 2006a, Abdelkrim Bourouihiya, Beurling weighted spaces, product-convolution
operators, and the tensor product of frames
35. 2006b, Aram Tangboondouangjit, Sigma-Delta quantization: number-theoretic
aspects of refining error estimates
36. 2007a, Somantika Datta, Wiener’s generalized harmonic analysis and wave-
form design
37. 2007b, Onur Oktay, Frame quantization theory and equiangular tight frames
38. 2008, David Widemann, Dimensionality reduction for hyperspectral data (Co-
adviser, W. Czaja)
39. 2009a, Matthew Hirn, Enumeration of harmonic frames and frame based
dimension reduction (Co-adviser, K. Okoudjou)
Wylie Dissertation Fellowship 2009
40. 2009b, Emily King, Wavelet and frame theory: frame bound gaps, general-
ized shearlets, Grassmannian fusion frames, and p-adic wavelets (Co-adviser,
W. Czaja)
Wylie Dissertation Fellowship 2008
John Benedetto’s Mathematical Work 9

41. 2010, Christopher Flake, The multiplicative Zak transform, dimension reduc-
tion, and wavelet analysis of LIDAR data (Co-adviser, W. Czaja)
42. 2011a, Enrico Au-Yeung, Balayage of Fourier transforms and the theory of
frames
43. 2011b, Avner Halevy, Extensions of Laplacian eigenmaps for manifold learning
(Co-adviser W. Czaja)
44. 2011c, Nathaniel Strawn, Geometric structures and optimization on finite
frames (Co-adviser, R. Balan)
45. 2012a, Kevin Duke, A study of the relationship between spectrum and geometry
through Fourier frames and Laplacian eigenmaps
46. 2012b, Alfredo Nava-Tudela, Image representation and compression via sparse
solutions of systems of linear equations
47. 2013, Rongrong Wang, Global geometric conditions on dictionaries for the
convergence of 1 minimization problems (Co-adviser W. Czaja)
48. 2014a, Travis Andrews, Frame multiplication theory for vector-valued har-
monic analysis
49. 2014b, Alex Cloninger, Exploiting data-dependent structure for improving
sensor acquisition and integration (Co-adviser W. Czaja)
Wylie Dissertation Fellowship 2013
NSF Postdoctoral Fellowship to Yale
50. 2014c, Tim Doster, Harmonic analysis inspired data fusion with applications
in remote sensing (Co-adviser W. Czaja)
51. 2014d, Wei-Hsuan Yu, Spherical two-distance sets and related topics in
harmonic analysis (Co-adviser A. Barg)
52. 2015a, Gokhan Civan, Identification of operators on elementary locally com-
pact abelian groups
53. 2015b, Paul Koprowski, Graph theoretic uncertainty principles
54. 2015c, James Murphy, Anisotropic harmonic analysis and integration of
remotely sensed data (Co-advisor W. Czaja)
55. 2016, Matthew Begué, Expedition in data and harmonic analysis on graphs
(Co-advisor K. Okoudjou)
56. 2018a, Weilin Li, Topics on harmonic analysis, sparse representations, and data
analysis (Co-advisor W. Czaja)
Wylie Dissertation Fellowship 2017
57. 2018b, Mark Magsino, Constant amplitude zero-autocorrelation sequences and
single pixel camera imaging
58. 2018c, Franck Njeunje, Computational methods in machine learning: transport
model, Haar wavelet, DNA classification, and MRI (Co-advisor W. Czaja)
59. 2020a, Shujie Kang, Generalized frame potential and problems related to SIC-
POVMs (Co-advisor K. Okoudjou)
60. 2020b, Chenzhi Zhao, Non-harmonic Fourier analysis and applications
61. 2020c, Kung-Ching Lin, Nonlinear sampling theory and efficient signal
recovery
10 D. Joyner

Fig. 3 Linear regression on the number of JB’s PhD students graduating per year

This is an average of about 1.2 PhD students per year. The list of pairs (year,
number of JB’s PhD students graduating that year) between 1971 and 2017 has best
linear fit14 y = ax + b, where a = 0.0451 . . ., b = −88.8937 . . .. In rough terms,
the number of PhD students JB graduates per year increases by about 4.5% per year.
The graph is in Fig. 3.

4 Papers

The majority of mathematical papers by JB deal with the representation of an

“arbitrary” function15 (typically on R or Rn and subject to some conditions), in
one way or another (by a Fourier series, wavelet expansion, integral transform, and
so on). The functions JB considers can be pretty general, but the point is that he
represents them for us in a nice way and then uses such a representation to derive

14 Again,thanks to SageMath.
15 Of course, the question “what’s a function?” immediately arises. Here, we include both
“generalized functions” (e.g., a distribution in the sense of Schwartz) and Radon measures as
functions.
John Benedetto’s Mathematical Work 11

Fig. 4 Linear regression on the number of JB’s papers published per year

something useful. In many of his papers, JB takes such a representation and either
(a) analyzes it to obtain estimates of a related quantity, or (b) applies it to an
engineering problem, or (c) uses it to investigate a question in another field such
as graph theory or analytic number theory.
Firstly, the list below includes some repetition (which I have tried to indicate).
For example, some “technical reports” were revised and then submitted to a journal
for publication. Secondly, some technical reports were not even submitted (e.g., they
might have a more expository flavor). Finally, we note that some papers have very
similar, or even identical, titles but are essentially unrelated (unless indicated).
Numerically, there is an average of about 3.48 papers per year. The list of pairs
(year, number of papers published that year) between 1965 and 2017 has best linear
fit16 y = ax + b, where a = 0.0708 . . ., b = −137.6162 . . .. In rough terms, the
number of papers JB publishes per year increases by about 7% per year. The graph
is in Fig. 4.

16 Thanks to the SageMath command find_fit.

12 D. Joyner

List of John J. Benedetto’s Published Papers

1965a. Representation theorem for the Fourier transform of integrable functions,

Bull. Soc. Roy. Sci. de Liege 9–10 (1965) 601–604.
1965b. Onto Criterion for adjoint maps, Bull. Soc. Roy. Sci. de Liege 9–10 (1965)
605–609.
1966a. Generalized Functions, Institute for Fluid Dynamics and Applied Math.,
BN–431 (1966) 1–380.
1966b. The Laplace transform of generalized functions, Canad. J. Math. 18 (1966),
357–374.
1967a. Tauberian translation algebras, Ann. di Mat. 74 (1967) 255–282.
1967b. Analytic representation of generalized functions, Math. Zeit. 97 (1967),
303–319.
1968a. Pseudo-measures and Harmonic Synthesis, University of Maryland,
Department of Mathematics Lecture Notes 5 (1968) 1–316.
1970a. A strong form of spectral resolution, Ann. di Mat. 86 (1970), 313–324.
1970b. Sets without true distributions, Bull. Soc. Roy. Sci. de Liege 7–8 (1970)
434–437.
1970c. Support preserving measure algebras and spectral synthesis, Math. Zeit.
118 (1970), 271–280.
1971a. Harmonic Analysis on Totally Disconnected Sets, Lecture Notes in
Mathematics, 202, Springer-Verlag, 1971.
1971b. Dirichlet series, spectral synthesis, and algebraic number fields, University
of Maryland, Department of Mathematics, TR 71–41 (1971) 1–23. (Also
referenced as Dirichlet series, spectral synthesis, and algebraic number
fields, Part I. There isn’t a part II, so I’ve used the shorter title.)
1971c. Trigonometric sums associated with pseudo-measures, Ann. Scuola Norm.
Sup., Pisa 25 (1971) 229–248.
1971d. Sui problemi di sintesi spettrale, Rend. Sem. Mat., Milano 4l (1971) 55–61.
1971e. Il Problema degli insiemi Helson-S, Rend. Sem. Mat., Milano 41 (1971)
63–68.
1971f. (LF) spaces and distributions on compact groups and spectral synthesis on
R/2π Z, Math. Ann.194 (1971) 52–67.
1972a. Measure zero: Two case studies, TR, 1972, 26 pages.
1972b. Ensembles de Helson et synthese spectrale, CRAS, Paris 274 (1972)
169–170.
1972c. Construction de fonctionnelles multiplicatives discontinues sur des algebres
metriques, CRAS, Paris 274 (1972) 254–256.
1972d. A support preserving Hahn-Banach property to determine Helson-S Sets,
Inventiones Math. 16 (1972) 214–228
1973a. Idele characters in spectral synthesis on R/2π Z, Ann. Inst. Fourier 23
(1973) 45–64.
1974a. Pseudo-measure energy and spectral synthesis, Can. J. Math. 26 (1974)
985–1001.
John Benedetto’s Mathematical Work 13

1974b. Tauberian theorems, Wiener’s spectrum, and spectral synthesis, Rend. Sem.
Mat., Milano 44 (1974) 63–73.
1975a. Spectral Synthesis, Pure and Applied Mathematics series, vol. 66, Aca-
demic Press, N.Y., 1975.
1975b. Zeta functions for idelic pseudo-measures, University of Maryland, Depart-
ment of Mathematics, TR 74–55 (1975) 1–46.
(Appeared as [1979a].)
1975c. The Wiener spectrum in spectral synthesis, Studies in Applied Math. (MIT)
54 (1975) 91–115
1977a. Analytic properties of idelic pseudo-measures, University of Maryland,
Department of Mathematics, TR 77–62 (1977) 1–33.
1977b. Idelic pseudo-measures and Dirichlet series, Symposia Mathematica, Aca-
demic Press, 1976 Conference on Harmonic Analysis, Rome 22 (1977)
205–222.
1979a. Zeta functions for idelic pseudo-measures, Ann. Scuola Norm. Sup., Pisa 6
(1979) 367–377.
1980a. Fourier analysis of Riemann distributions and explicit formulas, Math. Ann.
252 (1980) 141–164.
1981a. The role of Wiener’s Tauberian theorem in power spectrum computation,
University of Maryland, Department of Mathematics, TR 81–41 (1981)
1–44.
1981b. Spectral deconvolution, University of Maryland, Department of Mathemat-
ics, TR 81–63 (1981) 1–25.
1981c. The theory of constructive signal analysis, Studies in Applied Math. (MIT)
65 (1981) 37–80.
1981d. Wiener’s Tauberian theorem and the uncertainty principle, Proc. of Modern
Harmonic Analysis Conference 1982, Torino-Milano, (1983) 863–887.
1982a. A closure problem for signals in semigroup invariant systems, SIAM J.
Math. Analysis 13 (1982) 180–207.
1983a. Estimation problems and stochastic image analysis (with S. Belbas),
University of Maryland, Interdisciplinary Applied Mathematics Program,
TR89–67 (1983) 1–15.
(Note: While TR89-67 typically suggests this was written in 1989, this
report was written in 1983.)
1983b. Harmonic analysis and spectral estimation, J. Math. Analysis and Applica-
tions 91 (1983) 444–509.
1983c. Weighted Hardy spaces and the Laplace transform (with H. Heinig),
Cortona Conference 1982, Lecture Notes in Mathematics, 992, Springer-
Verlag, (1983) 240–277.
1983d. ‘ Wiener’s Tauberian theorem and the uncertainty principle, Proc. of Mod-
ern Harmonic Analysis Conference 1982, Torino-Milano, (1983) 863–887.
1984a. A local uncertainty principle, SIAM, J. Math. Analysis 15 (1984) 988–995.
1985a. An inequality associated with the uncertainty principle, Rend. Circ. Mat. di
Palermo 34 (1985) 407–421.
14 D. Joyner

1985b. Some mathematical methods for spectrum estimation, in Fourier Tech-

niques and Applications, J.F. Price, editor, Plenum Publishing (1985)
73–100.
1985c. Fourier uniqueness criteria and spectrum estimation theorems, in Fourier
Techniques and Applications, J.F. Price, editor, Plenum Publishing (1985)
149–172.
1986a. Inequalities for spectrum estimation, Linear Algebra and Applications 84
(1986) 377–383.
1986b. Weighted Hardy spaces and the Laplace transform II (with H. Heinig and R.
Johnson), Math. Nachrichten (Triebel commemorative volume), 132 (1987)
29–55.
1986c. Fourier inequalities with Ap weights (with H. Heinig and R. Johnson),
General Inequalities 5, Oberwolfach, (1986), ISNM 80 (1987) 217–232.
1987a. A quantitative maximum entropy theorem for the real line, Integral Equa-
tions and Operator Theory 10 (1987) 761–779.
1989a. Gabor representations and wavelets, AMS Contemporary Mathematics, 91
(1989) 9–27.
1989b. The Wiener-Plancherel formula in Euclidean space, (with G. Benke and W.
Evans), Advances in Applied Math., 10 (1989) 457–487.
(Note: This won the The Best Paper Award from the MITRE Corporation.)
1990a. Heisenberg wavelets and the uncertainty principle, Prometheus Inc., TR
(1990) 1–3.
1990b. Wavelet auditory models and irregular sampling, Prometheus Inc., TR
(1990) 1–6.
1990c. Uncertainty principle inequalities and spectrum estimation, NATO-ASI, in
Fourier Analysis and its Applications 1989, J. Byrnes, editor, Kluwer
Publishers, The Netherlands, Series C, 315 (1990) 143–182.
1990d. Irregular sampling and the theory of frames, I (with W. Heller), Mat. Note,
10, Suppl. no.1 (1990) 103–125.
(Note: There is no part II. This paper is mostly independent of [1992a]
and [1992f].)
1991a. Support dependent Fourier transform norm inequalities, (with C.
Karanikas), Rend. Sem. Mat., Roma, 11 (1991) 157–174.
1991b. The spherical Wiener-Plancherel formula and spectral estimation, SIAM
Math. Analysis, 22 (1991) 1110–1130.
1991c Fourier transform inequalities with measure weights, II
(with H. Heinig), Second International Conference on Function Spaces
1989,
Poznan, Poland, Teubner Texte zur Mathematik series, 120 (1991) 140–
151.
1991d. A multidimensional Wiener-Wintner theorem and spectrum estimation,
Trans. AMS, 327 (1991) 833–852.
1992a. Irregular sampling and the theory of frames, in The Role of Wavelets
in Signal Processing Applications, AFT Science and Research Center,
Wright-Patterson Air Force Base, TR (1992) 21–44.
John Benedetto’s Mathematical Work 15

1992b. Stationary frames and spectral estimation, NATO-ASI, in Probabilistic

and Stochastic Methods in Analysis, with Applications 1991, J. Byrnes,
editor, Kluwer Publishers, The Netherlands, Series C, (1992) 117–161.
1992c. Uncertainty principles for time-frequency operators (with C. Heil and D.
Walnut), Operator Theory: Advances and Applications, Birkhäuser, 58
(1992) 1–25.
1992d. An auditory motivated time-scale signal representation (with A. Teolis),
IEEE-SP International Symposium on Time-Frequency and Time-Scale
Analysis, (1992) 49–52.
1992e. Fourier transform inequalities with measure weights (with H. Heinig),
Advances in Math., 96 (1992) 194–225.
1992f. Irregular sampling and frames, in Wavelets - a Tutorial in Theory and
Applications, C. Chui, editor, Academic Press, Boston, (1992) 445–507.
1993a. Multiresolution analysis frames with applications (with S. Li), IEEE -
ICASSP, III (1993) 304–307.
1993b. On frames and filter banks (with S. Li), Conference on Information Sciences
and Systems, at The Johns Hopkins University, Technical Co-Sponsorship
with IEEE, 1993, invited.
1993c. A wavelet auditory model and data compression (with A. Teolis), Applied
and Computational Harmonic Analysis, 1(1993) 3–28.
1993d. Local frames (with A. Teolis), SPIE, Mathematical Imaging: Wavelet
Applications in Signal and Image Processing, 2034 (1993) 310–321.
1993e. Wavelets and sampling, in Wavelets and their Applications, spon-
sored/published by IEEE - South Australian Section, University of
Adelaide, The Flinders University, and the Research Centre for Sensor
Signal and Information Processing, (1993) 1–37.
1993f. From a wavelet auditory model to definitions of the Fourier transform,
NATO-ASI, in Wavelets and their Applications 1992, J. Byrnes, editor,
Kluwer Publishers, The Netherlands, Series C, (1993).
1994a. Noise reduction filters in mathematical models of biological systems, The
MITRE Corp., TR (1994) 1–6.
1994b. Noise reduction using frames, irregular sampling, and wavelets, ORD
Signal Processing, Fort Meade, MD, 1994.
1994c. Frame decompositions, sampling, and uncertainty principle inequalities, in
Wavelets: Mathematics and Applications, J. Benedetto and M. Frazier,
editors, CRC Press, Boca Raton, FL, (1994) 247–304.
1994d. Gabor frames for L2 and related spaces (with D. Walnut), in Wavelets:
Mathematics and Applications, J. Benedetto and M. Frazier, editors, CRC
Press, Boca Raton, FL (1994) 97–162.
1994e. Noise suppression using a wavelet model (with A. Teolis), IEEE - ICASSP
(1994).
1994f. Subband coding for sigmoidal nonlinear operations (with S. Saliani),
SPIE, Wavelet Applications, 2242 (1994) 19–27.
16 D. Joyner

1994g. Subband coding and noise reduction in multiresolution analysis frames

(with S. Li), SPIE, Wavelet Applications in Signal and Image Processing
II, 2303 (1994) 154–165.
1994h. The definition of the Fourier transform for weighted inequalities (with J.
Lakey), J. of Functional Analysis, 120 (1994) 403–439.
1994i. Analysis and feature extraction of epileptiform EEG waveforms (with D.
Colella, G. Jacyna, et al.), Fifth International Cleveland Clinic - Bethel
Epilepsy Symposium, 1994, Poster.
1994j. Narrow band frame multiresolution analysis with perfect reconstruction
(with Shidong Li), IEEE - SP International Symposium on Time-Frequency
and Time-Scale Analysis, (1994) 36–39.
1995a. Pyramidal Riesz products associated with subband coding and self-
similarity (with E. Bernstein), SPIE, Wavelet Applications for Dual Use,
2491 (1995) 212–221, invited.
1995b. Poisson’s summation formula in the construction of wavelet bases, with G.
Zimmermann, Proceedings of ICIAM, Hamburg, 1995, invited.
1995c. Wavelet-based analysis of EEG signals for detection and localization of
epileptic seizures (with G. Benke, M. Bozek-Kuzmicki, D. Colella, G.
Jacyna), SPIE, Wavelet Applications for Dual Use, 2491 (1995) 760–769.
1995d. Differentiation and the Balian-Low theorem (with C. Heil and D. Walnut),
J. of Fourier Analysis and Applications, 1 (1995) 355–402.
1995e. Wavelet analysis of spectrogram seizure chirps (with D. Colella), SPIE,
Wavelet Applications in Signal and Image Processing III, 2569 (1995) 512–
521, invited.
1995f. Local frames and noise reduction (with A. Teolis), Signal Processing, 45
(1995) 369–387.
1996a. Frame signal processing applied to biolectric data, in Wavelets in Biology
and Medicine, A. Aldroubi and M. Unser, editors, CRC Press, Inc., Boca
Raton, FL, 1996, Chapter 18, pages 467–486, invited.
1997a. Generalized harmonic analysis and Gabor and wavelet systems, AMS
Proceedings of Symposia in Applied Mathematics, volume 52, Wiener
Centenary Volume, 1997, pages 85–113, invited.
1997b. Sampling operators and the Poisson summation formula, (with G. Zimmer-
mann), Journal of Fourier Analysis and Applications, 3 (1997) 505–523.
1997c Wavelet detection of periodic behavior in EEG and ECoG data (with
G. Pfander), Proceedings of 15th IMACS World Congress on Scientific
Computation, Modelling, and Applied Mathematics, Berlin, 1 (1997) 75–
80, invited.
1998a. Gabor systems and the Balian-Low Theorem (with C. Heil and D. Walnut),
in Gabor Analysis and Algorithms, Theory and Applications, H. G.
Feichtinger and T. Strohmer, editors, Birkhäuser, Boston, 1998, pages
85–122, invited.
1998b. Noise reduction in terms of the theory of frames, in Signal and Image
Representation in Combined Spaces, J. Zeevi and R. Coifman, editors,
Academic Press, New York, 1998, pages 259–284, invited.
John Benedetto’s Mathematical Work 17

1998c. Self-similar pyramidal structures and signal reconstruction (with M. Leon

and S. Saliani), SPIE, Wavelet Applications V, 3391 (1998) 304–314,
invited.
1998d. The theory of multiresolution frames and applications to filter banks (with
S. Li), Applied and Computational Harmonic Analysis, 5 (1998), 389–427.
1998e. Frames, sampling, and seizure prediction, in Advances in Wavelets, K.-
S. Lau, editor, Springer-Verlag, New York, 1998, Chapter 1, pages 1–25,
invited.
1998f. Wavelet periodicity detection algorithms (with G. Pfander), SPIE, Wavelet
Applications in Signal and Image Processing VI, 3458 (1998), 48–55,
invited.
1999a. A multidimensional irregular sampling algorithm and applications (with
H.-C. Wu), IEEE - ICASSP, Phoenix, Special Session on Recent Advances
in Sampling Theory and Applications, 4 (1999), 4 pages, invited.
1999b. The construction of multiple dyadic minimally supported frequency
wavelets on Rd (with M. Leon), AMS Contemporary Math. Series, 247
(1999) 43–74.
1999c. A Beurling covering theorem and multidimensional irregular sampling
(with H.-C. Wu), in Sampling Theory and Applications, Loen, Norway,
sponsored/published by Norwegian University of Science and Technology,
(1999) 142–148, invited.
2000a. Sampling theory and wavelets, NATO-ASI, in Signal Processing for
Multimedia 1998, J. Byrnes, editor, Kluwer Publishers, The Netherlands,
2000, invited.
2000b. Ten books on wavelets, SIAM Review, 42 (2000) 127–138. (Although not a
research paper, JB was asked to write an extensive review of recent books
on wavelet theory. The result involved input from several of his graduate
students.)
2000c. Non-uniform sampling theory and spiral MRI reconstruction (with H.-C.
Wu), SPIE, Wavelet Applications in Signal and Image Processing VIII,
4119 (2000), invited.
2001a. The classical sampling theorem, and non-uniform sampling and frames
(with P.S.J.G. Ferreira), Chapter 1 of Modern Sampling Theory: Math-
ematics and Applications, J.J. Benedetto and P.S.J.G. Ferreira, editors,
Birkhäuser Boston, 2001.
2001b. Frames, irregular sampling, and a wavelet auditory model (with S. Scott),
Chapter 14 in Sampling Theory and Practice, F. Marvasti, editor, Kluwer
Academic/Plenum Publishers, New York, 2001, invited.
2001c. Wavelet frames: multiresolution analysis and extension principles (with O.
Treiber), Chapter 1 of Wavelet Transforms and Time-Frequency Signal
Analysis, L. Debnath, editor, Birkhäuser, Boston, 2001, 3–36, invited.
2001d. The construction of single wavelets in d-dimensions (with M. Leon), J.
Geometric Analysis, 11 (2001) 1–15.
2002a. MRI signal reconstruction by Fourier frames on interleaving spirals (with
A. Powell and H.-C. Wu), IEEE - ISBI 2002, 4 pages, invited.
18 D. Joyner

2002b. A fractal set constructed from a class of wavelet sets (with S. Sumetkijakan),
AMS Contemporary Math. Series, 313 (2002) 19–35.
2002c. Periodic wavelet transforms and periodicity detection (with G. Pfander),
SIAM J. Applied Math., 62 (2002) 1329–1368.
2003a. Finite normalized tight frames (with M. Fickus), Advances in Computa-
tional Math., 18 (2003) 357–385.
2003b. The Balian-Low theorem and regularity of Gabor systems (with W. Czaja,
P. Gadziński, and A. Powell), J. Geometric Analysis, 13 (2003) 239–254.
2003c. Weighted Fourier inequalities: new proof and generalization (with H.
Heinig), J. Fourier Analysis and Applications, 9 (2003) 1–37.
2003d. The Balian-Low theorem for symplectic forms (with W. Czaja and A.
Maltsev), Journal of Mathematical Physics, 44 (2003) 1735–1750.
2003e. Local sampling for regular wavelet and Gabor expansions (with N. Atreas
and C. Karanikas), Sampling Theory in Signal and Image processing, 2
(2003) 1–24
2003f. A Wiener-Wintner theorem for 1/f power spectra (with R. Kerby and S.
Scott), J. Math. Analysis and Applications, 279 (2003) 740–755.
2004a. Software package for CAZAC code generators and Doppler shift analysis
(with J. Donatelli and J. Ryan), 2004, see http://www.math.umd.edu/~jjb/
cazac.
2004b. Prologue for Sampling, Wavelets, and Tomography, J. J. Benedetto and
A. Zayed, editors, Birkhäuser, Boston, MA, 2004. (Although not a research
paper, this is longer than most prologues and contains new information on
sampling techniques and Claude Shannon.)
2004c. Constructive approximation in waveform design (invited) in Advances in
Constructive Approximation Theory, M. Neamtu and E. B. Saff, editors,
Nashboro Press, (2004) 89–108.
2004d. A wavelet theory for local fields and related groups (with R. L. Benedetto),
J. Geometric Analysis, 14(3) (2004) 423–456
2004e. Sigma-Delta quantization and finite frames (with A. Powell and Ö. Yilmaz),
ICASSP, Montreal, 2004, invited.
2005a. Multiscale Riesz products and their support properties (with E. Bernstein
and I. Konstantinidis), Acta Applicandae Math, 88(2) (2005) 201–227.
2005b. Analog to digital conversion for finite frames (with A. Powell and Ö.
Yilmaz), SPIE, Wavelet Applications in Signal and Image Processing
(2005), invited.
2005c. Greedy adaptive discrimination: component analysis by simultaneous
sparse approximation, (with J. Sieracki), SPIE, Wavelet Applications in
Signal and Image Processing (2005).
2005d. A (p, q)-version of Bourgain’s theorem (with A. Powell), Trans. Amer.
Math. Soc., 358 (2005) 2489–2505.
2006a. Tight frames and geometric properties of wavelet sets (with S. Sumetki-
jakan), Advances in Computational Math., 24 (2006) 35–56.
John Benedetto’s Mathematical Work 19

2006b. Geometrical properties of Grassmannian frames for R2 and R3 (with J.

Kolesar), EURASIP J. Applied Signal Processing, Special Issue on Frames
and Overcomplete Representations in Signal Processing (2006) 17 pages.
2006c. Sigma-Delta quantization and finite frames (with A. Powell and Ö. Yilmaz),
IEEE Trans. Information Theory, 52(5) (2006) 1990–2005.
2006d. Introduction for Fundamental Papers in Wavelet Theory, edited by C.
Heil and D. F. Walnut, Princeton University Press, 2006. (Although not a
research paper, this is an extensive, 20 page introduction for an important
volume.)
2006e. An endpoint (1, ∞) Balian-Low theorem (with W. Czaja, A. Powell, and J.
Sterbenz), Math. Research Letters, 13 (2006) 467–474.
2006f. An optimal example for the Balian-Low uncertainty principle, (with W.
Czaja and A. Powell), SIAM Journal of Mathematical Analysis, 38 (2006)
333–345.
2006g. Zero autocorrelation waveforms: a Doppler statistic and multifunction
problems (with J. Donatelli, I. Konstantinidis, and C. Shaw), ICASSP,
Toulouse, 2006, invited.
2006h. A Doppler statistic for zero autocorrelation waveforms (with J. Donatelli,
I. Konstantinidis, and C. Shaw), Conference on Information Sciences and
Systems, at Princeton University, Technical Co-Sponsorship with IEEE,
(2006), pages 1403–1407, invited.
2006i. Frame expansions for Gabor multipliers (with G. Pfander), Applied and
Computational Harmonic Analysis, 20 (2006) 26–40.
2006j. Second order Sigma-Delta quantization of finite frame expansions (with A.
Powell and Ö. Yilmaz), Applied and Computational Harmonic Analysis, 20
(2006) 128–148.
2007a. Ambiguity and sidelobe behavior of CAZAC waveforms (with A. Kebo, I.
Konstantinidis, M. Dellomo, J. Sieracki), IEEE Radar Conference, Boston
(2007).
2007b. The construction of d-dimensional MRA frames (with J. Romero), J.
Applied Functional Analysis, 2 (2007) 403–426.
2007c. Ambiguity function and frame theoretic properties of periodic zero autocor-
relation functions (with J. Donatelli), IEEE J. of Selected Topics in Signal
Processing, 1 (2007) 6–20.
2007d. Target tracking using particle filtering and CAZAC sequences (with I.
Kyriakides, I. Konstantinidis, D. Morrell, A. Papandreou-Suppappola),
IEEE International Waveform Diversity and Design, Pisa (2007), invited.
2007e. Concatenating codes for improved ambiguity behavior (with A. Bouroui-
hiya, I. Konstantinidis, and K. Okoudjou), Adaptive Waveform Tech-
nology for Futuristic Communications, Radar, and Navigation Systems,
International Conference on Electromagnetics in Advanced Applications
(ICEAA), Torino, 2007, invited.
2008a. The role of frame force in quantum detection (with A. Kebo), J. Fourier
Analysis and Applications, 14 (2008) 443–474.
20 D. Joyner

2008b. PCM-– comparison and sparse representation quantization (with O.

Oktay), Conference of Information Science and Systems, Princeton, 2008,
6 pages, invited.
2008c. Multiple target tracking using particle filtering and multicarrier phase-
coded CAZAC sequences (with I. Kyriakides, A. Papandreou-Suppappola,
D. Morrell, and I. Konstantinidis), Sensor, Signal and Information Process-
ing Workshop (SenSIP) 2008, Sedona AZ.
2008d. Human electrocortigraphic signature determination by eGAD sparse
approximation (with N. Crone and J. Sieracki), Sensor, Signal and
Information Processing Workshop (SenSIP) 2008, Sedona AZ.
2008e. Complex Sigma-Delta quantization algorithms for finite frames (with O.
Oktay and A. Tangboondouangjit), AMS Contemporary Mathematics, 464
(2008) 27–49.
2008f. Frames and a vector-valued ambiguity function (with J. Donatelli), IEEE -
Asilomar, 2008, invited.
2009a. Phase coded waveforms and their design - the role of the ambiguity function
(with I. Konstantinidis and M. Rangaswamy), IEEE Signal Processing
Magazine (invited), 26 (2009) 22–31.
2009b. Hadamard matrices and infinite unimodular sequences with 0-autocorrelation
(with S. Datta), IEEE International Waveform Diversity and Design 2009,
Orlando, invited, but withdrawn since the authors couldn’t attend the
conference.
(Note: See [2010c].)
2009c. Frame based kernel methods for automatic classification in hyperspectral
data (with W. Czaja, C. Flake, and M. Hirn), Proceedings IEEE-IGARSS
2009, invited.
2009d. Smooth functions associated with wavelet sets on Rd , d ≥ 1, and frame
bound gaps (with E. King), Acta Applicandae Math, 107 (2009) 121–142.
2009e. Geometric properties of Shapiro-Rudin polynomials (with J. Sugar-Moore),
Involve - A Journal of Mathematics, 2(4)(2009) 449–468.
2010a. Besov spaces for the Schrödinger operator with barrier potential (with S.
Zheng), Complex Analysis and Operator Theory, 4(4)(2010) 777–811.
2010b. Pointwise comparison of PCM and Sigma-Delta quantization (with O.
Oktay), Constructive Approximation, 32(1)(2010) 131–158.
2010c. Construction of infinite unimodular sequences with zero autocorrelation
(with S. Datta), Advances in Computational Mathematics, 32 (2010)
191–207.
2010d. Wavelet packets for multi- and hyper-spectral imagery (with W. Czaja, M.
Ehler, C. Flake, and M. Hirn), Wavelet Applications in Industrial Processing
VII, Proc. SPIE San Jose, 7535 (2010) 8–11.
2010e. Frame potential classification algorithm for retinal data (with W. Czaja
and M. Ehler), 26th Southern Biomedical Engineering Conference, College
Park, MD, 2010.
John Benedetto’s Mathematical Work 21

2010f. Maximally separated frames for automatic classification in hyperspectral

data (with W. Czaja, M. Ehler, and N. Strawn), IGARSS 2010, Honolulu,
preprint.
2011a. The construction of wavelet sets (with R. L. Benedetto) in Wavelets
and Multiscale Analysis, J. Cohen and A. I. Zayed, editors, Springer-
Birkhäuser, 2011, Chapter 2, pages 17–56.
2011b. Discrete autocorrelation-based multiplicative MRAs and sampling on R
(with. S. Datta), Sampling Theory in Signal and Image Processing 10 (2011)
111–133.
2011c. Intrinsic wavelet and frame applications (with T. Andrews), invited paper,
SPIE 2011, Orlando.
2012a. Image representation and compression via sparse solutions of systems of
linear equations (with A. Nava-Tudela), Technical Report, 2012. (Revised
and published in [2014f].)
2012b. Optimal ambiguity functions and Weil’s exponential sums bound (with R.
L. Benedetto and J. Woodworth), J. Fourier Analysis and Applications, 18
(2012) 471–487.
2012c. Constructions and a generalization of perfect autocorrelation sequences on
Z (with S. Datta), invited chapter in volume dedicated to Gil Walter, X.
Shen and A. Zayed, eds., Chapter 8, Springer (2012) 183–207.
2012d. Integration of heterogeneous data for classification in hyperspectral satel-
lite imagery (with W. Czaja, J. Dobrosotskaya, T. Doster, K. Duke, and D.
Gillis), SPIE 2012, Baltimore.
2012e. Semi-supervised learning of heterogeneous data in remote sensing imagery
(with W. Czaja, J. Dobrosotskaya, T. Doster, K. Duke, and D. Gillis), invited
paper SPIE 2012, Baltimore.
2013a. Balayage and short time Fourier transform frames (with E. Au-Yeung),
SampTA 2013 at Bremen, invited.
2013b. Wavelet packets for time-frequency analysis of multi-spectral images (with
W. Czaja and M. Ehler), International J. of Geomathematics, 4 (2013)
137–154.
2014a. Chandler Davis as mentor, Mathematical Intelligencer, 36 (2014) 20–21.
2014b. Wavelet packets and nonlinear manifold learning for analysis of hyper-
spectral data (with W. Czaja, T. Doster, and C. Schwartz), SPIE 2014,
Baltimore.
2014c. Operator-based integration of information in multimodal radiological
search mission with applications to anomaly detection (with A. Cloninger,
W. Czaja, T. Doster, B. Manning, T. McCullough, K. Kochersbeger, and M.
McLean), Proc. SPIE 9073, Chemical, Biological, Radiological, Nuclear,
and Explosives (CBRNE) Sensing XV, Baltimore, 2014.
2014d. Nonlinear dimensionality reduction via the ENH-LTSA method for hyper-
spectral image classification (with W. Czaja, A. Halevy, W. Li, C. Liu, B.
Shi, W. Sun, R. Wang), IEEE Journal of Selected Topics in Applied Earth
Observations and Remote Sensing (IEEE JSTARS), 7 (2014) 375–388.
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