Large Fourier Quasicrystals and Wiener’s Theorem

We find new simple conditions for a support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener’s Theorem on absolutely convergent trigonometric series and theory of almost periodic functions.

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Bibliographic Details
Published inThe Journal of fourier analysis and applications Vol. 25; no. 2; pp. 377 - 392
Main Author Favorov, S. Yu
Format Journal Article
LanguageEnglish
Published New York Springer US 15.04.2019
Springer
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Approximations and Expansions
Euclidean geometry
Euclidean space
Fourier Analysis
Lattices
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Periodic functions
Quasicrystals
Signal,Image and Speech Processing
Theorems
Almost periodic measure
52C23
42A75
Distribution
42B10
Fourier transform
Weiner’s Theorem
Spectrum of measure
Lattice
Measure with discrete support
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Summary:We find new simple conditions for a support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener’s Theorem on absolutely convergent trigonometric series and theory of almost periodic functions.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-017-9576-0