Mathematics – Functional Analysis
Scientific paper
2008-11-19
Mathematics
Functional Analysis
25 pages, LaTeX; added references and comments
Scientific paper
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. The structure of local and global minimizers of this potential is studied, when we restrict the frame potential 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. Thus, 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, varying the 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.
Massey Pedro
Ruiz Mariano
Stojanoff Demetrio
No associations
LandOfFree
The structure of minimizers of the frame potential on fusion frames does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The structure of minimizers of the frame potential on fusion frames, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The structure of minimizers of the frame potential on fusion frames will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-429481