The structure of minimizers of the frame potential on fusion frames

Autores
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the structure of local and global minimizers of this potential, when restricted to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vector frame case. Still, tight fusion frames are not as frequent as tight frames; indeed we show that there are choices of parameters involved in fusion frames for which no tight fusion frame can exist.We exhibit necessary and sufficient conditions for the existence of tight fusion frames with prescribed parameters, involving the so-called Horn-Klyachko’s compatibility inequalities. The second part of the work is devoted to the study of the minimization of the fusion frame potential on a fixed sequence of subspaces, with a varying sequence of weights. We related this problem to the index of the Hadamard product by positive matrices and use it to give different characterizations of these minima.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Materia
Fusion Frames
Frame Potential
Majorization
Hadamard Product
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19425
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The structure of minimizers of the frame potential on fusion framesMassey, Pedro GustavoRuiz, Mariano AndresStojanoff, DemetrioFusion FramesFrame PotentialMajorizationHadamard Producthttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the structure of local and global minimizers of this potential, when restricted to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vector frame case. Still, tight fusion frames are not as frequent as tight frames; indeed we show that there are choices of parameters involved in fusion frames for which no tight fusion frame can exist.We exhibit necessary and sufficient conditions for the existence of tight fusion frames with prescribed parameters, involving the so-called Horn-Klyachko’s compatibility inequalities. The second part of the work is devoted to the study of the minimization of the fusion frame potential on a fixed sequence of subspaces, with a varying sequence of weights. We related this problem to the index of the Hadamard product by positive matrices and use it to give different characterizations of these minima.Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaSpringer2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19425Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; The structure of minimizers of the frame potential on fusion frames; Springer; Journal Of Fourier Analysis And Applications; 16; 4; 8-2010; 514-5431069-5869CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-009-9098-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-009-9098-5info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0811.3159info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:33:56Zoai:ri.conicet.gov.ar:11336/19425instacron: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 10:33:56.781CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The structure of minimizers of the frame potential on fusion frames
title The structure of minimizers of the frame potential on fusion frames
spellingShingle The structure of minimizers of the frame potential on fusion frames
Massey, Pedro Gustavo
Fusion Frames
Frame Potential
Majorization
Hadamard Product
title_short The structure of minimizers of the frame potential on fusion frames
title_full The structure of minimizers of the frame potential on fusion frames
title_fullStr The structure of minimizers of the frame potential on fusion frames
title_full_unstemmed The structure of minimizers of the frame potential on fusion frames
title_sort The structure of minimizers of the frame potential on fusion frames
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 Fusion Frames
Frame Potential
Majorization
Hadamard Product
topic Fusion Frames
Frame Potential
Majorization
Hadamard Product
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 study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the structure of local and global minimizers of this potential, when restricted to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vector frame case. Still, tight fusion frames are not as frequent as tight frames; indeed we show that there are choices of parameters involved in fusion frames for which no tight fusion frame can exist.We exhibit necessary and sufficient conditions for the existence of tight fusion frames with prescribed parameters, involving the so-called Horn-Klyachko’s compatibility inequalities. The second part of the work is devoted to the study of the minimization of the fusion frame potential on a fixed sequence of subspaces, with a varying sequence of weights. We related this problem to the index of the Hadamard product by positive matrices and use it to give different characterizations of these minima.
Fil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Ruiz, Mariano Andres. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
description In this paper we study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the structure of local and global minimizers of this potential, when restricted to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vector frame case. Still, tight fusion frames are not as frequent as tight frames; indeed we show that there are choices of parameters involved in fusion frames for which no tight fusion frame can exist.We exhibit necessary and sufficient conditions for the existence of tight fusion frames with prescribed parameters, involving the so-called Horn-Klyachko’s compatibility inequalities. The second part of the work is devoted to the study of the minimization of the fusion frame potential on a fixed sequence of subspaces, with a varying sequence of weights. We related this problem to the index of the Hadamard product by positive matrices and use it to give different characterizations of these minima.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/19425
Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; The structure of minimizers of the frame potential on fusion frames; Springer; Journal Of Fourier Analysis And Applications; 16; 4; 8-2010; 514-543
1069-5869
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19425
identifier_str_mv Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio; The structure of minimizers of the frame potential on fusion frames; Springer; Journal Of Fourier Analysis And Applications; 16; 4; 8-2010; 514-543
1069-5869
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/article/10.1007/s00041-009-9098-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-009-9098-5
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0811.3159
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/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 13.069144

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