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- Title
Compactification of Infinite Graphs and Sampling.
- Authors
Jorgensen, Palle E. T.; Myung-Sin Song
- Abstract
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.
- Subjects
COMPACTIFICATION (Mathematics); GRAPH theory; SIGNAL sampling; HILBERT space; TRANSFER operators; WAVELETS (Mathematics)
- Publication
Sampling Theory in Signal & Image Processing, 2013, Vol 12, Issue 2/3, p139
- ISSN
1530-6429
- Publication type
Article
- DOI
10.1007/bf03549565