Multiplicative Lidskii's inequalities and optimal perturbations of frames

In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F = {f<SUB>j</SUB>}<SUB>j∈II<sub>n</sub></SUB> for double-struck C<SUP>d</SUP> we compute those dual frames G of F that are optimal perturbations of...

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Ruiz, Mariano Andrés, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2015
Materias:
Ciencias Exactas
Matemática
Convex potentials
Frames
Lidskii's inequality
Majorization
Perturbation of frames
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/86125
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-86125
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Matemática
Convex potentials
Frames
Lidskii's inequality
Majorization
Perturbation of frames
spellingShingle Ciencias Exactas
Matemática
Convex potentials
Frames
Lidskii's inequality
Majorization
Perturbation of frames
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
Multiplicative Lidskii's inequalities and optimal perturbations of frames
topic_facet Ciencias Exactas
Matemática
Convex potentials
Frames
Lidskii's inequality
Majorization
Perturbation of frames
description In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F = {f<SUB>j</SUB>}<SUB>j∈II<sub>n</sub></SUB> for double-struck C<SUP>d</SUP> we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V·F = {V f<SUB>j</SUB>}<SUB>j∈II<sub>n</sub></SUB> - for invertible operators V which are close to the identity - that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G = {gf<SUB>j</SUB>}<SUB>j∈II<sub>n</sub></SUB> that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.
format Articulo
Articulo
author Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
author_facet Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
author_sort Massey, Pedro Gustavo
title Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_short Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_full Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_fullStr Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_full_unstemmed Multiplicative Lidskii's inequalities and optimal perturbations of frames
title_sort multiplicative lidskii's inequalities and optimal perturbations of frames
publishDate 2015
url http://sedici.unlp.edu.ar/handle/10915/86125
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AT ruizmarianoandres multiplicativelidskiisinequalitiesandoptimalperturbationsofframes
AT stojanoffdemetrio multiplicativelidskiisinequalitiesandoptimalperturbationsofframes
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