2014/05/16 by Pedro Massey, Massey, Pedro G., Mariano Ruiz +3
Medicine · #15A60 #42C15 #Cell Adhesion Molecules Research #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.1405.4277
openalex publication_date 2014/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study two design problems in frame theory: on the one hand,\ngiven a fixed finite frame cF for hil\≅ Cd we compute those dual\nframes cG of cF that are optimal perturbations of the canonical dual\nframe for cF under certain restrictions on the norms of the elements of\n cG. On the other hand, for a fixed finite frame cF= fj j\∈ In for\n hil we compute those invertible operators V such that V^*V is a\nperturbation of the identity and such that the frame V\⋅\n cF= V ,fj j\∈ In - which is equivalent to cF - is optimal among\nsuch perturbations of cF. In both cases, optimality is measured with respect\nto submajorization of the eigenvalues of the frame operators. Hence, our\noptimal designs are minimizers of a family of convex potentials that include\nthe frame potential and the mean squared error. The key tool for these results\nis a multiplicative analogue of Lidskii's inequality in terms of\nlog-majorization and a characterization of the case of equality.\n