Optimal dual frames and frame completions for majorization

In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particul...

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Ruiz, Mariano Andrés, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2013
Materias:
Ciencias Exactas
Matemática
Dual frames
Frame completions
Frames
Majorization
Schur-Horn
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/85460
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-85460
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
Dual frames
Frame completions
Frames
Majorization
Schur-Horn
spellingShingle Ciencias Exactas
Matemática
Dual frames
Frame completions
Frames
Majorization
Schur-Horn
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
Optimal dual frames and frame completions for majorization
topic_facet Ciencias Exactas
Matemática
Dual frames
Frame completions
Frames
Majorization
Schur-Horn
description In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization. In particular, these optimal completions are the minimizers of a family of convex functionals that include the mean square error and the Benedetto-Fickus frame potential. On the other hand, given a fixed frame F we describe explicitly the spectral and geometrical structure of optimal frames G that are in duality with F and such that the Frobenius norms of their analysis operators is bounded from below by a fixed constant. In this case, optimality is measured with respect to submajorization of the frames operators. Our approach relies on the description of the spectral and geometrical structure of matrices that minimize submajorization on sets that are naturally associated with the problems above.
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 Optimal dual frames and frame completions for majorization
title_short Optimal dual frames and frame completions for majorization
title_full Optimal dual frames and frame completions for majorization
title_fullStr Optimal dual frames and frame completions for majorization
title_full_unstemmed Optimal dual frames and frame completions for majorization
title_sort optimal dual frames and frame completions for majorization
publishDate 2013
url http://sedici.unlp.edu.ar/handle/10915/85460
work_keys_str_mv AT masseypedrogustavo optimaldualframesandframecompletionsformajorization
AT ruizmarianoandres optimaldualframesandframecompletionsformajorization
AT stojanoffdemetrio optimaldualframesandframecompletionsformajorization
bdutipo_str Repositorios
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