Reducing and Invariant subspaces under two commuting shift operators
- Autores
- Aguilera Aguilera, Alejandra Patricia; Cabrelli, Carlos; Carbajal, D.; Paternostro, Victoria
- Año de publicación
- 2023
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this article, we characterize reducing and invariant subspaces of the space of square-integrable functions defined in the unit circle and having values in some Hardy space with multiplicity. We consider subspaces that reduce the bilateral shift and at the same time are invariant under the unilateral shift acting locally. We also study subspaces that reduce both operators. The conditions obtained are of the type of the ones in Helson and Beurling-Lax-Halmo´s theorems on characterizations of the invariance for the bilateral and unilateral shifts. The motivations for our study were inspired by recent results on Dynamical Sampling in shift-invariant spaces.
Fil: Aguilera Aguilera, Alejandra Patricia. 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: 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: Carbajal, D.. University Of Vienna; Austria
Fil: Paternostro, Victoria. 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 - Materia
-
Invariant subspaces
reducing subspaces
shift operators
Hardy spaces - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/231419
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Reducing and Invariant subspaces under two commuting shift operatorsAguilera Aguilera, Alejandra PatriciaCabrelli, CarlosCarbajal, D.Paternostro, VictoriaInvariant subspacesreducing subspacesshift operatorsHardy spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article, we characterize reducing and invariant subspaces of the space of square-integrable functions defined in the unit circle and having values in some Hardy space with multiplicity. We consider subspaces that reduce the bilateral shift and at the same time are invariant under the unilateral shift acting locally. We also study subspaces that reduce both operators. The conditions obtained are of the type of the ones in Helson and Beurling-Lax-Halmo´s theorems on characterizations of the invariance for the bilateral and unilateral shifts. The motivations for our study were inspired by recent results on Dynamical Sampling in shift-invariant spaces.Fil: Aguilera Aguilera, Alejandra Patricia. 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: 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: Carbajal, D.. University Of Vienna; AustriaFil: Paternostro, Victoria. 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"; ArgentinaAcademic Press Inc Elsevier Science2023-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/231419Aguilera Aguilera, Alejandra Patricia; Cabrelli, Carlos; Carbajal, D.; Paternostro, Victoria; Reducing and Invariant subspaces under two commuting shift operators; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 528; 1; 6-2023; 1-200022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022247X23004845info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2023.127481info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:55:29Zoai:ri.conicet.gov.ar:11336/231419instacron: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 09:55:30.153CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Reducing and Invariant subspaces under two commuting shift operators |
title |
Reducing and Invariant subspaces under two commuting shift operators |
spellingShingle |
Reducing and Invariant subspaces under two commuting shift operators Aguilera Aguilera, Alejandra Patricia Invariant subspaces reducing subspaces shift operators Hardy spaces |
title_short |
Reducing and Invariant subspaces under two commuting shift operators |
title_full |
Reducing and Invariant subspaces under two commuting shift operators |
title_fullStr |
Reducing and Invariant subspaces under two commuting shift operators |
title_full_unstemmed |
Reducing and Invariant subspaces under two commuting shift operators |
title_sort |
Reducing and Invariant subspaces under two commuting shift operators |
dc.creator.none.fl_str_mv |
Aguilera Aguilera, Alejandra Patricia Cabrelli, Carlos Carbajal, D. Paternostro, Victoria |
author |
Aguilera Aguilera, Alejandra Patricia |
author_facet |
Aguilera Aguilera, Alejandra Patricia Cabrelli, Carlos Carbajal, D. Paternostro, Victoria |
author_role |
author |
author2 |
Cabrelli, Carlos Carbajal, D. Paternostro, Victoria |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
Invariant subspaces reducing subspaces shift operators Hardy spaces |
topic |
Invariant subspaces reducing subspaces shift operators Hardy 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 |
In this article, we characterize reducing and invariant subspaces of the space of square-integrable functions defined in the unit circle and having values in some Hardy space with multiplicity. We consider subspaces that reduce the bilateral shift and at the same time are invariant under the unilateral shift acting locally. We also study subspaces that reduce both operators. The conditions obtained are of the type of the ones in Helson and Beurling-Lax-Halmo´s theorems on characterizations of the invariance for the bilateral and unilateral shifts. The motivations for our study were inspired by recent results on Dynamical Sampling in shift-invariant spaces. Fil: Aguilera Aguilera, Alejandra Patricia. 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: 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: Carbajal, D.. University Of Vienna; Austria Fil: Paternostro, Victoria. 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 |
description |
In this article, we characterize reducing and invariant subspaces of the space of square-integrable functions defined in the unit circle and having values in some Hardy space with multiplicity. We consider subspaces that reduce the bilateral shift and at the same time are invariant under the unilateral shift acting locally. We also study subspaces that reduce both operators. The conditions obtained are of the type of the ones in Helson and Beurling-Lax-Halmo´s theorems on characterizations of the invariance for the bilateral and unilateral shifts. The motivations for our study were inspired by recent results on Dynamical Sampling in shift-invariant spaces. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-06 |
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/11336/231419 Aguilera Aguilera, Alejandra Patricia; Cabrelli, Carlos; Carbajal, D.; Paternostro, Victoria; Reducing and Invariant subspaces under two commuting shift operators; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 528; 1; 6-2023; 1-20 0022-247X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/231419 |
identifier_str_mv |
Aguilera Aguilera, Alejandra Patricia; Cabrelli, Carlos; Carbajal, D.; Paternostro, Victoria; Reducing and Invariant subspaces under two commuting shift operators; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 528; 1; 6-2023; 1-20 0022-247X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022247X23004845 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2023.127481 |
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 |
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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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13.070432 |