Gabor orthonormal bases, tiling and periodicity

Alberto Debernardi Pinos; Nir Lev

doi:10.1007/s00208-021-02324-1

Gabor orthonormal bases, tiling and periodicity

Alberto Debernardi Pinos, Nir Lev

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that if the Gabor system { g(x- t) e²^πⁱ^s^x} , t∈ T, s∈ S, is an orthonormal basis in L²(R) and if the window function g is compactly supported, then both the time shift set T and the frequency shift set S must be periodic. To prove this we establish a necessary functional tiling type condition for Gabor orthonormal bases which may be of independent interest.

Original language	English
Pages (from-to)	1461-1467
Number of pages	7
Journal	Mathematische Annalen
Volume	384
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02324-1
State	Published - Dec 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-021-02324-1

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title = "Gabor orthonormal bases, tiling and periodicity",

abstract = "We show that if the Gabor system { g(x- t) e2πisx} , t∈ T, s∈ S, is an orthonormal basis in L2(R) and if the window function g is compactly supported, then both the time shift set T and the frequency shift set S must be periodic. To prove this we establish a necessary functional tiling type condition for Gabor orthonormal bases which may be of independent interest.",

author = "{Debernardi Pinos}, Alberto and Nir Lev",

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AU - Lev, Nir

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N2 - We show that if the Gabor system { g(x- t) e2πisx} , t∈ T, s∈ S, is an orthonormal basis in L2(R) and if the window function g is compactly supported, then both the time shift set T and the frequency shift set S must be periodic. To prove this we establish a necessary functional tiling type condition for Gabor orthonormal bases which may be of independent interest.

AB - We show that if the Gabor system { g(x- t) e2πisx} , t∈ T, s∈ S, is an orthonormal basis in L2(R) and if the window function g is compactly supported, then both the time shift set T and the frequency shift set S must be periodic. To prove this we establish a necessary functional tiling type condition for Gabor orthonormal bases which may be of independent interest.

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M3 - مقالة

SN - 0025-5831

VL - 384

SP - 1461

EP - 1467

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Gabor orthonormal bases, tiling and periodicity

Abstract

All Science Journal Classification (ASJC) codes

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