EXPLAIN A FEW OF THE IDEAS BEHIND THE FRAMES IN HILBERT AND BANACH SPACES IN RANDOM VARIABLES

Abstract

Several functional-analytical characteristics of these decompositions are established in this paper, and their relevance to wavelet and gabor systems is illustrated. We start by showing that atomic decompositions and frames are stable under small perturbations. This is driven by similar classical perturbation results for bases, like the Paley-Wiener basis stability criteria and the Kato perturbation theorem. The methodological contributions