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...
Guardado en:
Autores principales: | , , |
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Formato: | Articulo Preprint |
Lenguaje: | Inglés |
Publicado: |
2020
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Materias: | |
Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/124627 |
Aporte de: |
id |
I19-R120-10915-124627 |
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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 |
_version_ |
1764820450765963264 |