Potential theory on infinite products and locally compact groups
type: Item
instance of: scholarly article
title: Potential theory on infinite products and locally compact groups
zbMATH Open document ID: 0953.47029
DOI: 10.1023/A:1008654925672
author: Laurent Saloff-Coste
author: A. Bendikov
published in: Potential Analysis
publication date: 2001-01-17T00:00:00Z
review text: The paper is concerned with potential theory on a connected and locally connected locally compact group \(E\) of a countable basis topology. The aim is to study Bauer and Brelot translation invariant harmonic sheaves. The main result of the paper states that any such \(E\) carries an invariant Brelot harmonic sheaf and that every invariant elliptic Bauer harmonic sheaf is in fact a Brelot sheaf if and only if \(E\) is a finite dimensional Lie group. The proof is based upon a study of product diffusions on an infinite product of compact Riemannian manifolds.
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 31D05
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 1396417
zbMATH Keywords: harmonic spaces
zbMATH Keywords: Dirichlet spaces
zbMATH Keywords: Gaussian convolution semigroups
zbMATH Keywords: locally compact groups
zbMATH Keywords: Lie projective basis
zbMATH Keywords: potential theory
zbMATH Keywords: translation invariant harmonic sheaves
zbMATH Keywords: product diffusions
zbMATH Keywords: infinite product of compact Riemannian manifolds
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1396417