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Blair et al., 2019 - Google Patents

Logarithmic improvements in L^ p L p bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature

Blair et al., 2019

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Document ID
571616313890586805
Author
Blair M
Sogge C
Publication year
Publication venue
Inventiones mathematicae

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We consider the problem of proving L^ p L p bounds for eigenfunctions of the Laplacian in the high frequency limit in the presence of nonpositive curvature and more generally, manifolds without conjugate points. In particular, we prove estimates at the “critical …
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    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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    • G06—COMPUTING; CALCULATING; COUNTING
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    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/147—Discrete orthonormal transforms, e.g. discrete cosine transform, discrete sine transform, and variations therefrom, e.g. modified discrete cosine transform, integer transforms approximating the discrete cosine transform
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
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    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
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