Logarithmic Sobolev inequalities for pinned loop groups
type: Item
instance of: scholarly article
title: Logarithmic Sobolev inequalities for pinned loop groups
zbMATH Open document ID: 0859.22012
author: Bruce K. Driver
author: Terry Lohrenz
published in: Journal of Functional Analysis
publication date: 1996-10-13T00:00:00Z
review text: This is a detailed paper devoted to various geometric features of the infinite dimensional group \(L(G)\) of continuous based loops in a connected Lie group \(G\) of compact type. An \(\text{Ad}_G\)-invariant inner product in the algebra of \(G\) defines the so-called \(H^t\)-Riemannian structure on \(L(G)\). For this structure the authors construct a heat kernel associated to the Laplace-Beltrami operator and to a certain probability measure. A classical pre-Dirichlet form is constructed. It is shown that this form admits a logarithmic Sobolev inequality.
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 22E67
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 934262
zbMATH Keywords: loop group
zbMATH Keywords: Dirichlet form
zbMATH Keywords: Lie group
zbMATH Keywords: heat kernel
zbMATH Keywords: Laplace-Beltrami operator
zbMATH Keywords: Sobolev inequality
MaRDI profile type: Publication
OpenAlex ID: W2085568479
DOI: 10.1006/JFAN.1996.0113
description: scientific article; zbMATH DE number 934262