Duality in reconstruction systems

Autores
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider reconstruction systems (RS's), which are G-frames in a finite dimensional setting, and that includes the fusion frames as projective RS's. We describe the spectral picture of the set of RS operators for the projective systems with fixed weights. We also introduce a functional defined on dual pairs of RS's, called the joint potential, and study the structure of the minimizers of this functional. In the case of irreducible RS's the minimizers are characterize as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. At the end of the paper we show several examples that illustrate our results.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
DUAL RECONSTRUCTION SYSTEMS
FUSION FRAMES
RECONSTRUCTION SYSTEMS
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:11336/100297
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Duality in reconstruction systemsMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioDUAL RECONSTRUCTION SYSTEMSFUSION FRAMESRECONSTRUCTION SYSTEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider reconstruction systems (RS's), which are G-frames in a finite dimensional setting, and that includes the fusion frames as projective RS's. We describe the spectral picture of the set of RS operators for the projective systems with fixed weights. We also introduce a functional defined on dual pairs of RS's, called the joint potential, and study the structure of the minimizers of this functional. In the case of irreducible RS's the minimizers are characterize as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. At the end of the paper we show several examples that illustrate our results.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaElsevier Science Inc2012-02info: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/11336/100297Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Duality in reconstruction systems; Elsevier Science Inc; Linear Algebra and its Applications; 436; 3; 2-2012; 447-4640024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2011.02.022info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1007.0430info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S002437951100142Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:09:44Zoai:ri.conicet.gov.ar:11336/100297instacron: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 11:09:44.454CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Duality in reconstruction systems
title Duality in reconstruction systems
spellingShingle Duality in reconstruction systems
Massey, Pedro Gustavo
DUAL RECONSTRUCTION SYSTEMS
FUSION FRAMES
RECONSTRUCTION SYSTEMS
title_short Duality in reconstruction systems
title_full Duality in reconstruction systems
title_fullStr Duality in reconstruction systems
title_full_unstemmed Duality in reconstruction systems
title_sort Duality in reconstruction systems
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Ruiz, Mariano Andres
Stojanoff, Demetrio
author_role author
author2 Ruiz, Mariano Andres
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv DUAL RECONSTRUCTION SYSTEMS
FUSION FRAMES
RECONSTRUCTION SYSTEMS
topic DUAL RECONSTRUCTION SYSTEMS
FUSION FRAMES
RECONSTRUCTION SYSTEMS
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 consider reconstruction systems (RS's), which are G-frames in a finite dimensional setting, and that includes the fusion frames as projective RS's. We describe the spectral picture of the set of RS operators for the projective systems with fixed weights. We also introduce a functional defined on dual pairs of RS's, called the joint potential, and study the structure of the minimizers of this functional. In the case of irreducible RS's the minimizers are characterize as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. At the end of the paper we show several examples that illustrate our results.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We consider reconstruction systems (RS's), which are G-frames in a finite dimensional setting, and that includes the fusion frames as projective RS's. We describe the spectral picture of the set of RS operators for the projective systems with fixed weights. We also introduce a functional defined on dual pairs of RS's, called the joint potential, and study the structure of the minimizers of this functional. In the case of irreducible RS's the minimizers are characterize as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. At the end of the paper we show several examples that illustrate our results.
publishDate 2012
dc.date.none.fl_str_mv 2012-02
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/11336/100297
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Duality in reconstruction systems; Elsevier Science Inc; Linear Algebra and its Applications; 436; 3; 2-2012; 447-464
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100297
identifier_str_mv Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; Duality in reconstruction systems; Elsevier Science Inc; Linear Algebra and its Applications; 436; 3; 2-2012; 447-464
0024-3795
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2011.02.022
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1007.0430
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S002437951100142X
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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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