|May 23, 2014
|Southern Illinois University Edwardsville
We consider Hilbert spaces of functions on infinite graphs, and their compactifications. We arrived at a sampling formula in the spirit of Shannon; the idea is that we allow for sampling of functions f defined on a continuum completion of an infinite graph G, sampling the continuum by values of f at points in the graph G.
Rather than the more traditional frequency analysis of band-limited functions from Shannon, our analysis is instead based on reproducing kernel Hilbert spaces built from a prescribed infinite system of resistors on G.