On the Wiener semigroup and harmonic analysis on the infinite dimensional torus
type: Item
instance of: scholarly article
title: On the Wiener semigroup and harmonic analysis on the infinite dimensional torus
zbMATH Open document ID: 0657.35129
author: Thomas J. Taylor
published in: Acta Applicandae Mathematicae
publication date: 1987-01-01T00:00:00Z
review text: We present a model for which certain difficulties often associated with analysis on infinite-dimensional spaces do not occur. In this situation, the convolution semigroup of Wiener measures constructed by Gross becomes a self-adjoint contraction semigroup. We generalize a facet of Sobolev theory to our infinite-dimensional context, and consider the differentiability of Wiener measure in this new weak sense.
Mathematics Subject Classification ID: 35R20
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60G30
zbMATH DE Number: 4073628
zbMATH Keywords: infinite-dimensional analysis
zbMATH Keywords: Wiener measure
zbMATH Keywords: partial differential equations
zbMATH Keywords: analysis on infinite-dimensional spaces
zbMATH Keywords: convolution semigroup
zbMATH Keywords: Wiener measures
zbMATH Keywords: self-adjoint contraction semigroup
zbMATH Keywords: differentiability of Wiener measure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4073628