ARI Guest Talk: 14 June 2023
The classical frame potential in a finite dimensional Hilbert space was introduced by John J. Benedetto and Matthew Fickus and constitutes a fundamental tool for the study of tight frames with given norms. It is defined in terms of the Frobenius norm of the Gram operator associated to the elements of a frame. Minimizing the frame potential means to find those sequences that are “as orthogonal as possible”. Fusion frames are collections of closed subspaces and weights that allow to represent the elements of a Hilbert space from packets of coefficients. We study the fusion frame potential for the case that the weights and the dimensions of the subspaces are fixed and not necessarily equal. This potential is a generalization of the classical frame potential. We characterize its local (that are also global) minimizers which projections are eigenoperators of the fusion frame operator. We relate this result to the existence of tight fusion frames. This talk is based on a joint work with J. P. Llarena and P. Morillas.
Sigrid Heineken is a researcher at the Instituto de Investigaciones Matemáticas Luis A. Santaló (University of Buenos Aires-CONICET) and professor at the Department of Mathematics and Sciences of the University of San Andrés, Buenos Aires, Argentina. She received her Ph. D. in mathematics from the University of Buenos Aires and was a Marie-Curie postdoctoral fellow at the University of Vienna, Austria. Her research area is frame and fusion frame theory.