Extra Invariance of a Shift-Invariant Space in LCA Groups

Autores
Anastasio, Magalí; Cabrelli, Carlos; Paternostro, Victoria
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M" containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance.
Fil: Anastasio, Magalí. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Paternostro, Victoria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Shift-Invariant Space
Translation-Invariant Space
Lca Groups
Range Functions
Fiber Spaces
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:11336/15027
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15027
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Extra Invariance of a Shift-Invariant Space in LCA GroupsAnastasio, MagalíCabrelli, CarlosPaternostro, VictoriaShift-Invariant SpaceTranslation-Invariant SpaceLca GroupsRange FunctionsFiber Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M" containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance.Fil: Anastasio, Magalí. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Paternostro, Victoria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaElsevier2010-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15027Anastasio, Magalí; Cabrelli, Carlos; Paternostro, Victoria; Extra Invariance of a Shift-Invariant Space in LCA Groups; Elsevier; Journal Of Mathematical Analysis And Applications; 370; 2; 10-2010; 530-5370022-247Xenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X10004518info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2010.05.040info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:58:19Zoai:ri.conicet.gov.ar:11336/15027instacron: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:34982025-09-03 09:58:20.068CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Extra Invariance of a Shift-Invariant Space in LCA Groups
title Extra Invariance of a Shift-Invariant Space in LCA Groups
spellingShingle Extra Invariance of a Shift-Invariant Space in LCA Groups
Anastasio, Magalí
Shift-Invariant Space
Translation-Invariant Space
Lca Groups
Range Functions
Fiber Spaces
title_short Extra Invariance of a Shift-Invariant Space in LCA Groups
title_full Extra Invariance of a Shift-Invariant Space in LCA Groups
title_fullStr Extra Invariance of a Shift-Invariant Space in LCA Groups
title_full_unstemmed Extra Invariance of a Shift-Invariant Space in LCA Groups
title_sort Extra Invariance of a Shift-Invariant Space in LCA Groups
dc.creator.none.fl_str_mv Anastasio, Magalí
Cabrelli, Carlos
Paternostro, Victoria
author Anastasio, Magalí
author_facet Anastasio, Magalí
Cabrelli, Carlos
Paternostro, Victoria
author_role author
author2 Cabrelli, Carlos
Paternostro, Victoria
author2_role author
author
dc.subject.none.fl_str_mv Shift-Invariant Space
Translation-Invariant Space
Lca Groups
Range Functions
Fiber Spaces
topic Shift-Invariant Space
Translation-Invariant Space
Lca Groups
Range Functions
Fiber Spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M" containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance.
Fil: Anastasio, Magalí. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Cabrelli, Carlos. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Paternostro, Victoria. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of L2(G) is called K-invariant if it is invariant under translations by elements of K. Assume now that H is a countable uniform lattice in G and M is any closed subgroup of G containing H. In this article we study necessary and sufficient conditions for an H-invariant space to be M-invariant. As a consequence of our results we prove that for each closed subgroup M of G containing the lattice H, there exists an H-invariant space S that is exactly M-invariant. That is, S is not invariant under any other subgroup M" containing H. We also obtain estimates on the support of the Fourier transform of the generators of the H-invariant space, related to its M-invariance.
publishDate 2010
dc.date.none.fl_str_mv 2010-10
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/11336/15027
Anastasio, Magalí; Cabrelli, Carlos; Paternostro, Victoria; Extra Invariance of a Shift-Invariant Space in LCA Groups; Elsevier; Journal Of Mathematical Analysis And Applications; 370; 2; 10-2010; 530-537
0022-247X
url http://hdl.handle.net/11336/15027
identifier_str_mv Anastasio, Magalí; Cabrelli, Carlos; Paternostro, Victoria; Extra Invariance of a Shift-Invariant Space in LCA Groups; Elsevier; Journal Of Mathematical Analysis And Applications; 370; 2; 10-2010; 530-537
0022-247X
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/S0022247X10004518
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2010.05.040
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
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 13.13397

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