Local-to-global frames and applications to dynamical sampling problem

Abstract: In this paper we consider systems of vectors in a Hilbert space $\mathcal{H}$ of the form ${g_{jk}: j \in J, \, k\in K}\subset \mathcal{H}$ where $J$ and $K$ are countable sets of indices. We find conditions under which the local reconstruction properties of such a system extend to global stable recovery properties on the whole space. As a particular case, we obtain new local-to-global results for systems of type ${A^ng}_{g\in\mathcal{G},0\leq n\leq L }$ arising in the dynamical sampling problem.