Minimization of convex functionals over frame operators

2007/10/05 by Massey, Pedro, Ruiz, Mariano
#42C15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0710.1258

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.

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