Dynamical sampling and systems from iterative actions of operators

Abstract

In this chapter, we review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form {Ang: g ∈ G, n = 0, 1, 2, …}, where A is a bounded linear operator on a separable complex Hilbert space ℋ and G is a countable set of vectors in (Formula presented). The system of iterations mentioned above was motivated from the so-called dynamical sampling problem. In dynamical sampling, an unknown function f and its future states Anf are coarsely sampled at each time level n, 0 ≤ n < L, where A is an evolution operator that drives the system. The goal is to recover f from these space-time samples.