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

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 detec...

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Autores principales: Benac, María José, Massey, Pedro Gustavo, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2017
Materias:
Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/96588
https://ri.conicet.gov.ar/11336/66587
https://link.springer.com/article/10.1007%2Fs00041-016-9474-x
https://arxiv.org/abs/1508.01739
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-96588
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
spellingShingle Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
Benac, María José
Massey, Pedro Gustavo
Stojanoff, Demetrio
Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
topic_facet Matemática
Ciencias Exactas
Convex potentials
Frames of translates
Majorization
Oblique duality
Shift invariant subspaces
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.
format Articulo
Articulo
author Benac, María José
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_facet Benac, María José
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_sort Benac, María José
title Convex Potentials and Optimal Shift Generated Oblique Duals in Shift Invariant Spaces
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
publishDate 2017
url http://sedici.unlp.edu.ar/handle/10915/96588
https://ri.conicet.gov.ar/11336/66587
https://link.springer.com/article/10.1007%2Fs00041-016-9474-x
https://arxiv.org/abs/1508.01739
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AT masseypedrogustavo convexpotentialsandoptimalshiftgeneratedobliquedualsinshiftinvariantspaces
AT stojanoffdemetrio convexpotentialsandoptimalshiftgeneratedobliquedualsinshiftinvariantspaces
bdutipo_str Repositorios
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