Properties of finite dual fusion frames

Autores
Heineken, Sigrid Bettina; Morillas, Patricia Mariela
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert space, reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames. It is shown that for overcomplete fusion frames there always exist duals different from the canonical one. Conditions that assure the uniqueness of duals are given. The relation of dual fusion frame systems with dual frames and dual projective reconstruction systems is established. Optimal dual fusion frames for the reconstruction in case of erasures of subspaces, and optimal dual fusion frame systems for the reconstruction in case of erasures of local frame vectors are determined. Examples that illustrate the obtained results are exhibited.
Fil: Heineken, Sigrid Bettina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Materia
Frames
Fusion Frames
Dual Fusion Frames
Optimal Dual Fusion Frames
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:11336/31295
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Properties of finite dual fusion framesHeineken, Sigrid BettinaMorillas, Patricia MarielaFramesFusion FramesDual Fusion FramesOptimal Dual Fusion Frameshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert space, reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames. It is shown that for overcomplete fusion frames there always exist duals different from the canonical one. Conditions that assure the uniqueness of duals are given. The relation of dual fusion frame systems with dual frames and dual projective reconstruction systems is established. Optimal dual fusion frames for the reconstruction in case of erasures of subspaces, and optimal dual fusion frame systems for the reconstruction in case of erasures of local frame vectors are determined. Examples that illustrate the obtained results are exhibited.Fil: Heineken, Sigrid Bettina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaElsevier2014-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31295Heineken, Sigrid Bettina; Morillas, Patricia Mariela; Properties of finite dual fusion frames; Elsevier; Linear Algebra and its Applications; 453; 7-2014; 1-270024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1509.07724info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379514002225info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2014.04.008info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:10Zoai:ri.conicet.gov.ar:11336/31295instacron: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 09:56:11.159CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Properties of finite dual fusion frames
title Properties of finite dual fusion frames
spellingShingle Properties of finite dual fusion frames
Heineken, Sigrid Bettina
Frames
Fusion Frames
Dual Fusion Frames
Optimal Dual Fusion Frames
title_short Properties of finite dual fusion frames
title_full Properties of finite dual fusion frames
title_fullStr Properties of finite dual fusion frames
title_full_unstemmed Properties of finite dual fusion frames
title_sort Properties of finite dual fusion frames
dc.creator.none.fl_str_mv Heineken, Sigrid Bettina
Morillas, Patricia Mariela
author Heineken, Sigrid Bettina
author_facet Heineken, Sigrid Bettina
Morillas, Patricia Mariela
author_role author
author2 Morillas, Patricia Mariela
author2_role author
dc.subject.none.fl_str_mv Frames
Fusion Frames
Dual Fusion Frames
Optimal Dual Fusion Frames
topic Frames
Fusion Frames
Dual Fusion Frames
Optimal Dual Fusion Frames
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert space, reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames. It is shown that for overcomplete fusion frames there always exist duals different from the canonical one. Conditions that assure the uniqueness of duals are given. The relation of dual fusion frame systems with dual frames and dual projective reconstruction systems is established. Optimal dual fusion frames for the reconstruction in case of erasures of subspaces, and optimal dual fusion frame systems for the reconstruction in case of erasures of local frame vectors are determined. Examples that illustrate the obtained results are exhibited.
Fil: Heineken, Sigrid Bettina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Morillas, Patricia Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
description A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert space, reinforcing the idea that this concept of duality solves the question about an appropriate definition of dual fusion frames. It is shown that for overcomplete fusion frames there always exist duals different from the canonical one. Conditions that assure the uniqueness of duals are given. The relation of dual fusion frame systems with dual frames and dual projective reconstruction systems is established. Optimal dual fusion frames for the reconstruction in case of erasures of subspaces, and optimal dual fusion frame systems for the reconstruction in case of erasures of local frame vectors are determined. Examples that illustrate the obtained results are exhibited.
publishDate 2014
dc.date.none.fl_str_mv 2014-07
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/11336/31295
Heineken, Sigrid Bettina; Morillas, Patricia Mariela; Properties of finite dual fusion frames; Elsevier; Linear Algebra and its Applications; 453; 7-2014; 1-27
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31295
identifier_str_mv Heineken, Sigrid Bettina; Morillas, Patricia Mariela; Properties of finite dual fusion frames; Elsevier; Linear Algebra and its Applications; 453; 7-2014; 1-27
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/url/https://arxiv.org/abs/1509.07724
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379514002225
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2014.04.008
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
application/pdf
application/pdf
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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