Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces

Autores
Benac, María José; Massey, Pedro Gustavo; Stojanoff, Demetrio
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce extensions of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in L2(Rk). We show that under a natural normalization hypothesis, these convex potentials detect tight frames as their minimizers. We obtain a detailed spectral analysis of the frame operators of shift generated oblique duals of a fixed frame of translates. We use this result to obtain the spectral and geometrical structure of optimal shift generated oblique duals with norm restrictions, that simultaneously minimize every convex potential; we approach this problem by showing that the water-filling construction in probability spaces is optimal with respect to submajorization (within an appropriate set of functions) and by considering a non-commutative version of this construction for measurable fields of positive operators.
Departamento de Matemáticas
Materia
Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/96588
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/96588
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant SpacesBenac, María JoséMassey, Pedro GustavoStojanoff, DemetrioMatemáticaCiencias ExactasConvex potentialsFrames of translatesMajorizationOblique dualityShift invariant subspacesWe introduce extensions of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in L2(Rk). We show that under a natural normalization hypothesis, these convex potentials detect tight frames as their minimizers. We obtain a detailed spectral analysis of the frame operators of shift generated oblique duals of a fixed frame of translates. We use this result to obtain the spectral and geometrical structure of optimal shift generated oblique duals with norm restrictions, that simultaneously minimize every convex potential; we approach this problem by showing that the water-filling construction in probability spaces is optimal with respect to submajorization (within an appropriate set of functions) and by considering a non-commutative version of this construction for measurable fields of positive operators.Departamento de Matemáticas2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf401-441http://sedici.unlp.edu.ar/handle/10915/96588enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/66587info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00041-016-9474-xinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1508.01739info:eu-repo/semantics/altIdentifier/issn/1069-5869info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-016-9474-xinfo:eu-repo/semantics/altIdentifier/hdl/11336/66587info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/2.5/ar/Creative Commons Attribution-NonCommercial-NoDerivs 2.5 Argentina (CC BY-NC-ND 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:20:20Zoai:sedici.unlp.edu.ar:10915/96588Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:20:21.054SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
title Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
spellingShingle Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
Benac, María José
Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
title_short Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
title_full Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
title_fullStr Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
title_full_unstemmed Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
title_sort Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
dc.creator.none.fl_str_mv Benac, María José
Massey, Pedro Gustavo
Stojanoff, Demetrio
author Benac, María José
author_facet Benac, María José
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
topic Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
dc.description.none.fl_txt_mv We introduce extensions of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in L2(Rk). We show that under a natural normalization hypothesis, these convex potentials detect tight frames as their minimizers. We obtain a detailed spectral analysis of the frame operators of shift generated oblique duals of a fixed frame of translates. We use this result to obtain the spectral and geometrical structure of optimal shift generated oblique duals with norm restrictions, that simultaneously minimize every convex potential; we approach this problem by showing that the water-filling construction in probability spaces is optimal with respect to submajorization (within an appropriate set of functions) and by considering a non-commutative version of this construction for measurable fields of positive operators.
Departamento de Matemáticas
description We introduce extensions of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in L2(Rk). We show that under a natural normalization hypothesis, these convex potentials detect tight frames as their minimizers. We obtain a detailed spectral analysis of the frame operators of shift generated oblique duals of a fixed frame of translates. We use this result to obtain the spectral and geometrical structure of optimal shift generated oblique duals with norm restrictions, that simultaneously minimize every convex potential; we approach this problem by showing that the water-filling construction in probability spaces is optimal with respect to submajorization (within an appropriate set of functions) and by considering a non-commutative version of this construction for measurable fields of positive operators.
publishDate 2017
dc.date.none.fl_str_mv 2017-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/96588
url http://sedici.unlp.edu.ar/handle/10915/96588
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/66587
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00041-016-9474-x
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1508.01739
info:eu-repo/semantics/altIdentifier/issn/1069-5869
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-016-9474-x
info:eu-repo/semantics/altIdentifier/hdl/11336/66587
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Creative Commons Attribution-NonCommercial-NoDerivs 2.5 Argentina (CC BY-NC-ND 2.5)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Creative Commons Attribution-NonCommercial-NoDerivs 2.5 Argentina (CC BY-NC-ND 2.5)
dc.format.none.fl_str_mv application/pdf
401-441
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.070432

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