Minimization of convex functionals over frame operators

Abstract. We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the frame operator of a set of vectors which is close to the original one.

• Type: Journal
• Year: 2010
• Where: ADCM
• Authors: Pedro Massey, Mariano Ruiz
• Keywords: ADCM 2010, Convex Functionals, Finite Dimensional Hilbert, Frame Operator