Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups

We prove the existence of sampling sets and interpolation sets near the critical density, in Paley Wiener spaces of a locally compact abelian (LCA) group G. This solves a problem left by Gröchenig, Kutyniok, and Seip (2008) [7]. To achieve this result, we prove the existence of universal Riesz bases...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Agora, E., Antezana, J., Cabrelli, C.
Formato: JOUR
Materias:
Beurling's densities
Dyadic cubes
Interpolation
Locally compact abelian groups
Multi-tiling
Riesz bases
Sampling
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00018708_v285_n_p454_Agora
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00018708_v285_n_p454_Agora
record_format dspace
spelling todo:paper_00018708_v285_n_p454_Agora2023-10-03T13:52:20Z Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups Agora, E. Antezana, J. Cabrelli, C. Beurling's densities Dyadic cubes Interpolation Locally compact abelian groups Multi-tiling Riesz bases Sampling We prove the existence of sampling sets and interpolation sets near the critical density, in Paley Wiener spaces of a locally compact abelian (LCA) group G. This solves a problem left by Gröchenig, Kutyniok, and Seip (2008) [7]. To achieve this result, we prove the existence of universal Riesz bases of characters for L2(Ω), provided that the relatively compact subset Ω of the dual group Ĝ satisfies a multi-tiling condition. This last result generalizes Fuglede's theorem, and extends to LCA groups setting recent constructions of Riesz bases of exponentials in bounded sets of Rd. © 2015 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00018708_v285_n_p454_Agora
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Beurling's densities
Dyadic cubes
Interpolation
Locally compact abelian groups
Multi-tiling
Riesz bases
Sampling
spellingShingle Beurling's densities
Dyadic cubes
Interpolation
Locally compact abelian groups
Multi-tiling
Riesz bases
Sampling
Agora, E.
Antezana, J.
Cabrelli, C.
Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
topic_facet Beurling's densities
Dyadic cubes
Interpolation
Locally compact abelian groups
Multi-tiling
Riesz bases
Sampling
description We prove the existence of sampling sets and interpolation sets near the critical density, in Paley Wiener spaces of a locally compact abelian (LCA) group G. This solves a problem left by Gröchenig, Kutyniok, and Seip (2008) [7]. To achieve this result, we prove the existence of universal Riesz bases of characters for L2(Ω), provided that the relatively compact subset Ω of the dual group Ĝ satisfies a multi-tiling condition. This last result generalizes Fuglede's theorem, and extends to LCA groups setting recent constructions of Riesz bases of exponentials in bounded sets of Rd. © 2015 Elsevier Inc.
format JOUR
author Agora, E.
Antezana, J.
Cabrelli, C.
author_facet Agora, E.
Antezana, J.
Cabrelli, C.
author_sort Agora, E.
title Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
title_short Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
title_full Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
title_fullStr Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
title_full_unstemmed Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
title_sort multi-tiling sets, riesz bases, and sampling near the critical density in lca groups
url http://hdl.handle.net/20.500.12110/paper_00018708_v285_n_p454_Agora
work_keys_str_mv AT agorae multitilingsetsrieszbasesandsamplingnearthecriticaldensityinlcagroups
AT antezanaj multitilingsetsrieszbasesandsamplingnearthecriticaldensityinlcagroups
AT cabrellic multitilingsetsrieszbasesandsamplingnearthecriticaldensityinlcagroups
_version_ 1807323336038940672

Ejemplares similares