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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/158541
Ver los metadatos del registro completo
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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. |
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2021 |
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2021-04-27 |
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publishedVersion |
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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 |
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http://hdl.handle.net/11336/158541 |
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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 |
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