Stochastic analysis on product manifolds: Dirichlet operators on differential forms
type: Item
instance of: scholarly article
title: Stochastic analysis on product manifolds: Dirichlet operators on differential forms
zbMATH Open document ID: 0970.58020
author: Alexei Daletskii
author: S. Albeverio
author: Yuri Kondratiev
published in: Journal of Functional Analysis
publication date: 2001-10-10T00:00:00Z
review text: Consider a product manifold \(\mathbf M\), namely an infinite product of identical compact Riemannian manifolds. The aim of this work is to study the differential calculus on \(\mathbf M\), and to deduce a construction of Dirichlet operators on differential forms. More precisely, the analogues of Bochner and de Rham operators are defined. Properties of the corresponding semigroups are obtained by a probabilistic technique, more precisely by considering stochastic differential equations on tensor bundles over \(\mathbf M\). Finally, this study is related to Gibbs measures on \(\mathbf M\).
reviewed by: Jean Picard
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 58B99
Mathematics Subject Classification ID: 31C25
zbMATH DE Number: 1529986
zbMATH Keywords: stochastic analysis on manifolds
zbMATH Keywords: Bochner Laplacian
zbMATH Keywords: de Rham Laplacian
zbMATH Keywords: Dirichlet operators
zbMATH Keywords: Gibbs measures
MaRDI profile type: Publication
full work available at URL: jfan.2000.3629
OpenAlex ID: W2070545787
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DOI: 10.1006/JFAN.2000.3629
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description: scientific article; zbMATH DE number 1529986