Existence of quasicrystals and universal stable sampling and interpolation in LCA groups

Autores
Agora, Elona; Antezana, Jorge Abel; Cabrelli, Carlos; Matei, Basarab
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated with the cut and project scheme that produces it. On the other hand, if an LCA group G admits a simple quasicrystal, we prove that recent results of Meyer and Matei for the case of the Euclidean space R^n can be extended to G. More precisely, we prove that simple quasicrystals are universal sets of stable sampling and universal sets of stable interpolation in generalized Paley-Wiener spaces.
Fil: Agora, Elona. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Matei, Basarab. Universite de Paris 13-Nord; Francia
Materia
QUASICRYSTALS
UNIVERSAL SAMPLING AND INTERPOLATION
LANDAU BEURLING'S DENSITIES
POISSON MEASURES
LOCALLY COMPACT ABELIAN GROUPS
LCA GROUPS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/106615
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/106615
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Existence of quasicrystals and universal stable sampling and interpolation in LCA groupsAgora, ElonaAntezana, Jorge AbelCabrelli, CarlosMatei, BasarabQUASICRYSTALSUNIVERSAL SAMPLING AND INTERPOLATIONLANDAU BEURLING'S DENSITIESPOISSON MEASURESLOCALLY COMPACT ABELIAN GROUPSLCA GROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated with the cut and project scheme that produces it. On the other hand, if an LCA group G admits a simple quasicrystal, we prove that recent results of Meyer and Matei for the case of the Euclidean space R^n can be extended to G. More precisely, we prove that simple quasicrystals are universal sets of stable sampling and universal sets of stable interpolation in generalized Paley-Wiener spaces.Fil: Agora, Elona. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Matei, Basarab. Universite de Paris 13-Nord; FranciaAmerican Mathematical Society2019-05info: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/11336/106615Agora, Elona; Antezana, Jorge Abel; Cabrelli, Carlos; Matei, Basarab; Existence of quasicrystals and universal stable sampling and interpolation in LCA groups; American Mathematical Society; Transactions Of The American Mathematical Society; 372; 7; 5-2019; 4647-46740002-99471088-6850CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/tran/0000-000-00/S0002-9947-2019-07723-1/info:eu-repo/semantics/altIdentifier/doi/10.1090/tran/7723info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1611.05804info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:56:37Zoai:ri.conicet.gov.ar:11336/106615instacron: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 09:56:37.548CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
title Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
spellingShingle Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
Agora, Elona
QUASICRYSTALS
UNIVERSAL SAMPLING AND INTERPOLATION
LANDAU BEURLING'S DENSITIES
POISSON MEASURES
LOCALLY COMPACT ABELIAN GROUPS
LCA GROUPS
title_short Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
title_full Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
title_fullStr Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
title_full_unstemmed Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
title_sort Existence of quasicrystals and universal stable sampling and interpolation in LCA groups
dc.creator.none.fl_str_mv Agora, Elona
Antezana, Jorge Abel
Cabrelli, Carlos
Matei, Basarab
author Agora, Elona
author_facet Agora, Elona
Antezana, Jorge Abel
Cabrelli, Carlos
Matei, Basarab
author_role author
author2 Antezana, Jorge Abel
Cabrelli, Carlos
Matei, Basarab
author2_role author
author
author
dc.subject.none.fl_str_mv QUASICRYSTALS
UNIVERSAL SAMPLING AND INTERPOLATION
LANDAU BEURLING'S DENSITIES
POISSON MEASURES
LOCALLY COMPACT ABELIAN GROUPS
LCA GROUPS
topic QUASICRYSTALS
UNIVERSAL SAMPLING AND INTERPOLATION
LANDAU BEURLING'S DENSITIES
POISSON MEASURES
LOCALLY COMPACT ABELIAN GROUPS
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 characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated with the cut and project scheme that produces it. On the other hand, if an LCA group G admits a simple quasicrystal, we prove that recent results of Meyer and Matei for the case of the Euclidean space R^n can be extended to G. More precisely, we prove that simple quasicrystals are universal sets of stable sampling and universal sets of stable interpolation in generalized Paley-Wiener spaces.
Fil: Agora, Elona. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Matei, Basarab. Universite de Paris 13-Nord; Francia
description We characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated with the cut and project scheme that produces it. On the other hand, if an LCA group G admits a simple quasicrystal, we prove that recent results of Meyer and Matei for the case of the Euclidean space R^n can be extended to G. More precisely, we prove that simple quasicrystals are universal sets of stable sampling and universal sets of stable interpolation in generalized Paley-Wiener spaces.
publishDate 2019
dc.date.none.fl_str_mv 2019-05
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/11336/106615
Agora, Elona; Antezana, Jorge Abel; Cabrelli, Carlos; Matei, Basarab; Existence of quasicrystals and universal stable sampling and interpolation in LCA groups; American Mathematical Society; Transactions Of The American Mathematical Society; 372; 7; 5-2019; 4647-4674
0002-9947
1088-6850
CONICET Digital
CONICET
url http://hdl.handle.net/11336/106615
identifier_str_mv Agora, Elona; Antezana, Jorge Abel; Cabrelli, Carlos; Matei, Basarab; Existence of quasicrystals and universal stable sampling and interpolation in LCA groups; American Mathematical Society; Transactions Of The American Mathematical Society; 372; 7; 5-2019; 4647-4674
0002-9947
1088-6850
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/tran/0000-000-00/S0002-9947-2019-07723-1/
info:eu-repo/semantics/altIdentifier/doi/10.1090/tran/7723
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1611.05804
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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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