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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/66587
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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 Técnicas2025-09-29T10:04:24Zoai: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:34982025-09-29 10:04:25.033CONICET 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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13.070432 |