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

Autores
Cabrelli, Carlos; Antezana, Jorge Abel; Agora, Elona
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Agora, Elona. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
Materia
Sampling
Interpolation
Critical Density
Lca Groups
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/3380
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groupsCabrelli, CarlosAntezana, Jorge AbelAgora, ElonaSamplingInterpolationCritical DensityLca Groupshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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.Fil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaFil: Agora, Elona. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; ArgentinaAcademic Press Inc Elsevier Science2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/3380Cabrelli, Carlos; Antezana, Jorge Abel; Agora, Elona; Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 285; 11-2015; 454-4770001-8708enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0001870815002960info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2015.08.006info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:32:48Zoai:ri.conicet.gov.ar:11336/3380instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:32:48.542CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
title Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
spellingShingle Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
Cabrelli, Carlos
Sampling
Interpolation
Critical Density
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
dc.creator.none.fl_str_mv Cabrelli, Carlos
Antezana, Jorge Abel
Agora, Elona
author Cabrelli, Carlos
author_facet Cabrelli, Carlos
Antezana, Jorge Abel
Agora, Elona
author_role author
author2 Antezana, Jorge Abel
Agora, Elona
author2_role author
author
dc.subject.none.fl_str_mv Sampling
Interpolation
Critical Density
Lca Groups
topic Sampling
Interpolation
Critical Density
Lca Groups
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Agora, Elona. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina
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.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/3380
Cabrelli, Carlos; Antezana, Jorge Abel; Agora, Elona; Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 285; 11-2015; 454-477
0001-8708
url http://hdl.handle.net/11336/3380
identifier_str_mv Cabrelli, Carlos; Antezana, Jorge Abel; Agora, Elona; Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 285; 11-2015; 454-477
0001-8708
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0001870815002960
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2015.08.006
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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