Iterative actions of normal operators

Abstract

Let A be a normal operator in a Hilbert space H, and let G subset of H be a countable set of vectors. We investigate the relations between A, G and L that make the system of iterations {A(n)g : g is an element of G, 0 <= n < L(g)} complete, Bessel, a basis, or a frame for H. The problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis, including, frame theory and spectral theory. It also has relations to topics in applied harmonic analysis including, wavelet theory and time-frequency analysis. (C) 2016 Elsevier Inc. All rights reserved.