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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
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
© 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
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!
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.
“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
Part I Introduction
John Benedetto’s Mathematical Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
David Joyner
xv
xvi Contents
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Contributors
xvii
xviii Contributors
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
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
(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
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
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.
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
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
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.
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
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
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