2016/06/09 by Akram Aldroubi, Aldroubi, Akram, Armenak Petrosyan +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #46N99 (Primary) 42C15 #94O20 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1606.03136
openalex publication_date 2016/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 operators on a separable complex Hilbert space H and G is a countable set of vectors in H . 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.