The structure of group preserving operators

Autores
Barbieri, Davide; Cabrelli, Carlos; Carbajal, Diana Agustina; Hernández Rodríguez, Eugenio; Molter, Ursula Maria
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of 2() where is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group Γ which is a semi-direct product of a uniform lattice of with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be Γ preserving. i.e. they commute with the action of Γ. In particular, we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where is the Euclidean space.
Fil: Barbieri, Davide. Universidad Autónoma de Madrid; España
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, Diana Agustina. 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: Hernández Rodríguez, Eugenio. Universidad Autónoma de Madrid; España
Fil: Molter, Ursula Maria. 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
Parseval frames
Normal Operators
Diagonlization
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:11336/158541
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/158541
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The structure of group preserving operatorsBarbieri, DavideCabrelli, CarlosCarbajal, Diana AgustinaHernández Rodríguez, EugenioMolter, Ursula MariaInvariant SubspacesParseval framesNormal OperatorsDiagonlizationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of 2() where is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group Γ which is a semi-direct product of a uniform lattice of with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be Γ preserving. i.e. they commute with the action of Γ. In particular, we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where is the Euclidean space.Fil: Barbieri, Davide. Universidad Autónoma de Madrid; EspañaFil: 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, Diana Agustina. 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: Hernández Rodríguez, Eugenio. Universidad Autónoma de Madrid; EspañaFil: Molter, Ursula Maria. 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"; ArgentinaSpringer2021-04-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/158541Barbieri, Davide; Cabrelli, Carlos; Carbajal, Diana Agustina; Hernández Rodríguez, Eugenio; Molter, Ursula Maria; The structure of group preserving operators; Springer; Sampling Theory, Signal Processing, and Data Analysis; 19; 1; 27-4-2021; 1-222730-57162730-5724CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s43670-021-00005-3info:eu-repo/semantics/altIdentifier/doi/10.1007/s43670-021-00005-3info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2009.12551info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:00:24Zoai:ri.conicet.gov.ar:11336/158541instacron: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:34982025-10-22 12:00:24.502CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The structure of group preserving operators
title The structure of group preserving operators
spellingShingle The structure of group preserving operators
Barbieri, Davide
Invariant Subspaces
Parseval frames
Normal Operators
Diagonlization
title_short The structure of group preserving operators
title_full The structure of group preserving operators
title_fullStr The structure of group preserving operators
title_full_unstemmed The structure of group preserving operators
title_sort The structure of group preserving operators
dc.creator.none.fl_str_mv Barbieri, Davide
Cabrelli, Carlos
Carbajal, Diana Agustina
Hernández Rodríguez, Eugenio
Molter, Ursula Maria
author Barbieri, Davide
author_facet Barbieri, Davide
Cabrelli, Carlos
Carbajal, Diana Agustina
Hernández Rodríguez, Eugenio
Molter, Ursula Maria
author_role author
author2 Cabrelli, Carlos
Carbajal, Diana Agustina
Hernández Rodríguez, Eugenio
Molter, Ursula Maria
author2_role author
author
author
author
dc.subject.none.fl_str_mv Invariant Subspaces
Parseval frames
Normal Operators
Diagonlization
topic Invariant Subspaces
Parseval frames
Normal Operators
Diagonlization
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 paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of 2() where is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group Γ which is a semi-direct product of a uniform lattice of with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be Γ preserving. i.e. they commute with the action of Γ. In particular, we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where is the Euclidean space.
Fil: Barbieri, Davide. Universidad Autónoma de Madrid; España
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, Diana Agustina. 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: Hernández Rodríguez, Eugenio. Universidad Autónoma de Madrid; España
Fil: Molter, Ursula Maria. 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 paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of 2() where is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group Γ which is a semi-direct product of a uniform lattice of with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be Γ preserving. i.e. they commute with the action of Γ. In particular, we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where is the Euclidean space.
publishDate 2021
dc.date.none.fl_str_mv 2021-04-27
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/11336/158541
Barbieri, Davide; Cabrelli, Carlos; Carbajal, Diana Agustina; Hernández Rodríguez, Eugenio; Molter, Ursula Maria; The structure of group preserving operators; Springer; Sampling Theory, Signal Processing, and Data Analysis; 19; 1; 27-4-2021; 1-22
2730-5716
2730-5724
CONICET Digital
CONICET
url http://hdl.handle.net/11336/158541
identifier_str_mv Barbieri, Davide; Cabrelli, Carlos; Carbajal, Diana Agustina; Hernández Rodríguez, Eugenio; Molter, Ursula Maria; The structure of group preserving operators; Springer; Sampling Theory, Signal Processing, and Data Analysis; 19; 1; 27-4-2021; 1-22
2730-5716
2730-5724
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://link.springer.com/10.1007/s43670-021-00005-3
info:eu-repo/semantics/altIdentifier/doi/10.1007/s43670-021-00005-3
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2009.12551
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 12.982451

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