Sampling solutions of Schrödinger equations on combinatorial graphs

Abstract

We consider functions on a graph $G$ whose evolution in time $-\infty <t<\infty$ is governed by a Schrödinger type equation with a combinatorial Laplace operator on the right side. For a given subset $S$ of vertices of $G$ we compute a cut-off frequency $\omega >0$ such that solutions to a Cauchy problem with initial data in $P{W}_{\omega }(G)$ are completely determined by their samples on $S\times \{k\pi /\omega \},$ where $k\in \mathbf{N}$. It is shown that in the case of a bipartite graph our results are sharp.

submitted