Compactification of Infinite Graphs and Sampling
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چکیده
In the paper, we consider Hilbert spaces of functions on infinite graphs, and their compactifications. We arrive 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.
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تاریخ انتشار 2014