Tiling functions and Gabor orthonormal basis

We study the existence of Gabor orthonormal bases with window the characteristic function of the set Ω = [ 0 , α ] ∪ [ β + α , β + 1 ] of measure 1, with α , β > 0 . By the symmetries of the problem, we can restrict our attention to the case α ≤ 1 / 2 . We prove that either if α 1 / 2 or ( α = 1...

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Detalles Bibliográficos
Autores principales:	Agora, Elona, Antezana, Jorge Abel, Kolountzakis, Mihail N.
Formato:	Articulo Preprint
Lenguaje:	Inglés
Publicado:	2020
Materias:	Matemática Spectral sets Fuglede's conjecture Tilings Packings Gabor basis
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/124627
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-124627
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Matemática Spectral sets Fuglede's conjecture Tilings Packings Gabor basis
spellingShingle	Matemática Spectral sets Fuglede's conjecture Tilings Packings Gabor basis Agora, Elona Antezana, Jorge Abel Kolountzakis, Mihail N. Tiling functions and Gabor orthonormal basis
topic_facet	Matemática Spectral sets Fuglede's conjecture Tilings Packings Gabor basis
description	We study the existence of Gabor orthonormal bases with window the characteristic function of the set Ω = [ 0 , α ] ∪ [ β + α , β + 1 ] of measure 1, with α , β > 0 . By the symmetries of the problem, we can restrict our attention to the case α ≤ 1 / 2 . We prove that either if α 1 / 2 or ( α = 1 / 2 and β ≥ 1 / 2 ) there exist such Gabor orthonormal bases, with window the characteristic function of the set Ω, if and only if Ω tiles the line. Furthermore, in both cases, we completely describe the structure of the set of time–frequency shifts associated to these bases.
format	Articulo Preprint
author	Agora, Elona Antezana, Jorge Abel Kolountzakis, Mihail N.
author_facet	Agora, Elona Antezana, Jorge Abel Kolountzakis, Mihail N.
author_sort	Agora, Elona
title	Tiling functions and Gabor orthonormal basis
title_short	Tiling functions and Gabor orthonormal basis
title_full	Tiling functions and Gabor orthonormal basis
title_fullStr	Tiling functions and Gabor orthonormal basis
title_full_unstemmed	Tiling functions and Gabor orthonormal basis
title_sort	tiling functions and gabor orthonormal basis
publishDate	2020
url	http://sedici.unlp.edu.ar/handle/10915/124627
work_keys_str_mv	AT agoraelona tilingfunctionsandgabororthonormalbasis AT antezanajorgeabel tilingfunctionsandgabororthonormalbasis AT kolountzakismihailn tilingfunctionsandgabororthonormalbasis
bdutipo_str	Repositorios
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Tiling functions and Gabor orthonormal basis

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