The structure of minimizers of the frame potential on fusion frames

In this paper we study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the structure of local and global minimizers of this potential, when restricted to suitable sets of fusion frames. T...

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Ruiz, Mariano Andrés, Stojanoff, Demetrio
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2010
Materias:
Matemática
Fusion frames
Frame potential
Majorization
Hadamard product
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101839
https://ri.conicet.gov.ar/11336/19425
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-101839
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Fusion frames
Frame potential
Majorization
Hadamard product
spellingShingle Matemática
Fusion frames
Frame potential
Majorization
Hadamard product
Massey, Pedro Gustavo
Ruiz, Mariano Andrés
Stojanoff, Demetrio
The structure of minimizers of the frame potential on fusion frames
topic_facet Matemática
Fusion frames
Frame potential
Majorization
Hadamard product
description In this paper we study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. We study the structure of local and global minimizers of this potential, when restricted to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vector frame case. Still, tight fusion frames are not as frequent as tight frames; indeed we show that there are choices of parameters involved in fusion frames for which no tight fusion frame can exist.We exhibit necessary and sufficient conditions for the existence of tight fusion frames with prescribed parameters, involving the so-called Horn-Klyachko’s compatibility inequalities. The second part of the work is devoted to the study of the minimization of the fusion frame potential on a fixed sequence of subspaces, with a varying sequence of weights. We related this problem to the index of the Hadamard product by positive matrices and use it to give different characterizations of these minima.
format Articulo
Preprint
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 The structure of minimizers of the frame potential on fusion frames
title_short The structure of minimizers of the frame potential on fusion frames
title_full The structure of minimizers of the frame potential on fusion frames
title_fullStr The structure of minimizers of the frame potential on fusion frames
title_full_unstemmed The structure of minimizers of the frame potential on fusion frames
title_sort structure of minimizers of the frame potential on fusion frames
publishDate 2010
url http://sedici.unlp.edu.ar/handle/10915/101839
https://ri.conicet.gov.ar/11336/19425
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