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.
Categories: math.FA