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dc.contributor.author
Benac, Maria Jose
dc.contributor.author
Massey, Pedro Gustavo
dc.contributor.author
Stojanoff, Demetrio
dc.date.available
2018-12-17T18:50:10Z
dc.date.issued
2017-04
dc.identifier.citation
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
dc.identifier.issn
1069-5869
dc.identifier.uri
http://hdl.handle.net/11336/66587
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Birkhauser Boston Inc
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
Convex Potentials
dc.subject
Frames of Translates
dc.subject
Majorization
dc.subject
Oblique Duality
dc.subject
Shift Invariant Subspaces
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-11-12T13:21:53Z
dc.journal.volume
23
dc.journal.number
2
dc.journal.pagination
401-441
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Boston
dc.description.fil
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
dc.description.fil
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
dc.description.fil
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
dc.journal.title
Journal Of Fourier Analysis And Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00041-016-9474-x
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00041-016-9474-x
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1508.01739
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