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Title: Gabor orthonormal bases, tiling and periodicity
Author: Pinos, Alberto Debernardi
Lev, Nir
Issue Date: 2022
Publisher: Springer
Abstract: We show that if the Gabor system $\{g(x − t)e^{2\pi isx}, t\in T,s\in S\}$, is an orthonormal basis in $L^2(\mathbb{R})$ 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.
Peer review: yes
DOI: 10.1007/s00208-021-02324-1
ISSN: 0025-5831
Publisher Version:
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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