Journal article
A sampling theory for infinite weighted graphs
Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, Vol.31(2), pp.209-236
2011
DOI: 10.7494/OpMath.2011.31.2.209
Appears in Diamond Open Access
Abstract
We prove two sampling theorems for infinite (countable discrete) weighted graphs \(G\); one example being "large grids of resistors" i.e., networks and systems of resistors. We show that there is natural ambient continuum \(X\) containing \(G\), and there are Hilbert spaces of functions on \(X\) that allow interpolation by sampling values of the functions restricted only on the vertices in \(G\). We sample functions on \(X\) from their discrete values picked in the vertex-subset \(G\). We prove two theorems that allow for such realistic ambient spaces \(X\) for a fixed graph \(G\), and for interpolation kernels in function Hilbert spaces on \(X\), sampling only from points in the subset of vertices in \(G\). A continuum is often not apparent at the outset from the given graph \(G\). We will solve this problem with the use of ideas from stochastic integration.
Details
- Title: Subtitle
- A sampling theory for infinite weighted graphs
- Creators
- Palle Jorgensen
- Resource Type
- Journal article
- Publication Details
- Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica, Vol.31(2), pp.209-236
- DOI
- 10.7494/OpMath.2011.31.2.209
- ISSN
- 1232-9274
- Language
- English
- Date published
- 2011
- Academic Unit
- Mathematics
- Record Identifier
- 9983985945402771
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