On the minimizers of the fusion frame potential

TL;DR

This paper investigates the minimizers of the fusion frame potential with fixed weights and subspace dimensions, characterizing local and global minimizers as eigenoperators of the fusion frame operator and relating to tight fusion frames.

Contribution

It generalizes classical vector frame potential results to fusion frames with fixed weights and dimensions, introducing the concept of irregularity for minimizer characterization.

Findings

Minimizers are eigenoperators of the fusion frame operator.

Characterization of local and global minimizers using irregularity.

Connection established between minimizers and the existence of tight fusion frames.

Abstract

We study the minimizers of the fusion frame potential in the case that both the weights and the dimensions of the subspaces are fixed and not necessarily equal. Using a concept of irregularity we provide a description of the local (that are also global) minimizers which projections are eigenoperators of the fusion frame operator. This result will be related to the existence of tight fusion frames. In this way we generalize results known for the classical vector frame potential.