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

Autores
Benac, Maria Jose; 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.
Fil: Benac, Maria Jose. 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: 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: Stojanoff, Demetrio. 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
Materia
CONVEX POTENTIALS
FRAMES OF TRANSLATES
MAJORIZATION
OBLIQUE DUALITY
SHIFT INVARIANT SUBSPACES
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:11336/66587
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/66587
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant SpacesBenac, Maria JoseMassey, Pedro GustavoStojanoff, DemetrioCONVEX POTENTIALSFRAMES OF TRANSLATESMAJORIZATIONOBLIQUE DUALITYSHIFT INVARIANT SUBSPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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.Fil: Benac, Maria Jose. 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: 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: Stojanoff, Demetrio. 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; ArgentinaBirkhauser Boston Inc2017-04info: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/11336/66587Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 23; 2; 4-2017; 401-4411069-5869CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-016-9474-xinfo: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/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:34:10Zoai:ri.conicet.gov.ar:11336/66587instacron: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 11:34:10.902CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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, Maria Jose
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, Maria Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author Benac, Maria Jose
author_facet Benac, Maria Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv CONVEX POTENTIALS
FRAMES OF TRANSLATES
MAJORIZATION
OBLIQUE DUALITY
SHIFT INVARIANT SUBSPACES
topic CONVEX POTENTIALS
FRAMES OF TRANSLATES
MAJORIZATION
OBLIQUE DUALITY
SHIFT INVARIANT SUBSPACES
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 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.
Fil: Benac, Maria Jose. 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: 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: Stojanoff, Demetrio. 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
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
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/11336/66587
Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 23; 2; 4-2017; 401-441
1069-5869
CONICET Digital
CONICET
url http://hdl.handle.net/11336/66587
identifier_str_mv Benac, Maria Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio; Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 23; 2; 4-2017; 401-441
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/doi/10.1007/s00041-016-9474-x
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
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 Birkhauser Boston Inc
publisher.none.fl_str_mv Birkhauser Boston 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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