A sampling theory for infinite weighted graphs

Abstract

Tyt. z nagł.References p. 234-236.Dostępny również w formie drukowanej.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. KEYWORDS: weighted graph, Hilbert space, Laplace operator, sampling, Shannon, white noise, Wiener transform, interpolation

Similar works

Full text

thumbnail-image

Academic Digital Library (Akademickiej Bibliotece Cyfrowej)

redirect
Last time updated on 01/07/2013

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.