Journal article
Compactification of Infinite Graphs and Sampling
Sampling theory in signal and image processing, Vol.12(2-3), pp.139-158
05/01/2013
DOI: 10.1007/BF03549565
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
.
Details
- Title: Subtitle
- Compactification of Infinite Graphs and Sampling
- Creators
- Palle E. T Jorgensen - University of IowaMyung-Sin Song - Southern Illinois University Edwardsville
- Resource Type
- Journal article
- Publication Details
- Sampling theory in signal and image processing, Vol.12(2-3), pp.139-158
- Publisher
- Springer International Publishing
- DOI
- 10.1007/BF03549565
- ISSN
- 1530-6429
- Language
- English
- Date published
- 05/01/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9984240765702771
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