IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
The structure of minimizers of the frame potential on fusion frames
Autor/es:
MASSEY, PEDRO G; RUIZ, MARIANO; STOJANOFF, DEMETRIO
Revista:
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
Editorial:
BIRKHAUSER BOSTON INC
Referencias:
Año: 2009 p. 1 - 1
ISSN:
1069-5869
Resumen:
In this paper we study the fusion frame potential that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the fi nite-dimensional fusion frame setting. We stydy 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 di fferent characterizations of these minima.