Optimal dual frames and frame completions for majorization

Autores
Stojanoff, Demetrio; Ruiz, M; Massey, Pedro Gustavo
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto?Fickusʼ frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, M. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Materia
Dual Frames
Frame Completions
Majorization
Schur-Horn
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:11336/3278
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/3278
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimal dual frames and frame completions for majorizationStojanoff, DemetrioRuiz, MMassey, Pedro GustavoDual FramesFrame CompletionsMajorizationSchur-Hornhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto?Fickusʼ frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, M. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; ArgentinaFil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaAcademic Press Inc Elsevier Science2013-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/3278Stojanoff, Demetrio; Ruiz, M; Massey, Pedro Gustavo; Optimal dual frames and frame completions for majorization; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 34; 2; 3-2013; 201-2231063-5203enginfo:eu-repo/semantics/altIdentifier/url/http://arxiv.org/pdf/1108.4412v3.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:09:53Zoai:ri.conicet.gov.ar:11336/3278instacron: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 10:09:53.595CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal dual frames and frame completions for majorization
title Optimal dual frames and frame completions for majorization
spellingShingle Optimal dual frames and frame completions for majorization
Stojanoff, Demetrio
Dual Frames
Frame Completions
Majorization
Schur-Horn
title_short Optimal dual frames and frame completions for majorization
title_full Optimal dual frames and frame completions for majorization
title_fullStr Optimal dual frames and frame completions for majorization
title_full_unstemmed Optimal dual frames and frame completions for majorization
title_sort Optimal dual frames and frame completions for majorization
dc.creator.none.fl_str_mv Stojanoff, Demetrio
Ruiz, M
Massey, Pedro Gustavo
author Stojanoff, Demetrio
author_facet Stojanoff, Demetrio
Ruiz, M
Massey, Pedro Gustavo
author_role author
author2 Ruiz, M
Massey, Pedro Gustavo
author2_role author
author
dc.subject.none.fl_str_mv Dual Frames
Frame Completions
Majorization
Schur-Horn
topic Dual Frames
Frame Completions
Majorization
Schur-Horn
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 consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto?Fickusʼ frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Ruiz, M. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
description In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto?Fickusʼ frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
publishDate 2013
dc.date.none.fl_str_mv 2013-03
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/11336/3278
Stojanoff, Demetrio; Ruiz, M; Massey, Pedro Gustavo; Optimal dual frames and frame completions for majorization; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 34; 2; 3-2013; 201-223
1063-5203
url http://hdl.handle.net/11336/3278
identifier_str_mv Stojanoff, Demetrio; Ruiz, M; Massey, Pedro Gustavo; Optimal dual frames and frame completions for majorization; Academic Press Inc Elsevier Science; Applied And Computational Harmonic Analysis; 34; 2; 3-2013; 201-223
1063-5203
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/pdf/1108.4412v3.pdf
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 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
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
_version_ 1844613982565957632
score 13.070432

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