Finite sensor Dynamical Sampling

CABRELLI, C.; MOLTER U.; PATERNOSTRO, V.; PHILIPP, F.

Tallin

Congreso; 12th International Conference on Sampling Theory and Applications; 2017

SampTa

Dynamical Sampling aims to subsample solutions of linear dynamical systems at various times. One way to model this consists of considering inner products of the form 〈h,Anfi〉, where h is the signal, (fi) a system of fixed vectors and A a linear operator which is connected with the dynamical system. Here, we characterize those systems (Anfi)n∈ℕ, i∈I with finite index sets I and normal operators A which are frames for the underlying Hilbert space. It turns out that this problem is intimately connected with spectral properties of the operator A and complex analysis in the unit disk. We also provide conditions on the spectral properties of A* for non-normal A.