Abstract

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.

Original languageEnglish (US)
Pages (from-to)131-143
Number of pages13
JournalActa Applicandae Mathematicae
Volume10
Issue number2
DOIs
StatePublished - Oct 1987

Fingerprint

Wiener Measure
Harmonic analysis
Harmonic Analysis
Convolution
Torus
Semigroup
Convolution Semigroup
Contraction Semigroup
Infinite-dimensional Spaces
Differentiability
Gross
Facet
Generalise
Model
Context

Keywords

  • AMS subject classifications: 35RJ20, 60B15, 60G30
  • Infinite-dimensional analysis
  • partial differential equations
  • Wiener measure

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Cite this

On the Wiener semigroup and harmonic analysis on the infinite dimensional torus. / Taylor, Thomas.

In: Acta Applicandae Mathematicae, Vol. 10, No. 2, 10.1987, p. 131-143.

Research output: Contribution to journalArticle

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