On the Wiener semigroup and harmonic analysis on the infinite dimensional torus

Thomas Taylor

doi:10.1007/BF00046616

On the Wiener semigroup and harmonic analysis on the infinite dimensional torus

Thomas Taylor

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Pages (from-to)	131-143
Number of pages	13
Journal	Acta Applicandae Mathematicae
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/BF00046616
State	Published - Oct 1987

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

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10.1007/BF00046616

Cite this

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title = "On the Wiener semigroup and harmonic analysis on the infinite dimensional torus",

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.",

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

author = "Thomas Taylor",

year = "1987",

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AU - Taylor, Thomas

PY - 1987/10

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N2 - 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.

AB - 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.

KW - AMS subject classifications: 35RJ20, 60B15, 60G30

KW - Infinite-dimensional analysis

KW - Wiener measure

KW - partial differential equations

UR - https://www.scopus.com/pages/publications/34250107565

UR - https://www.scopus.com/pages/publications/34250107565#tab=citedBy

U2 - 10.1007/BF00046616

DO - 10.1007/BF00046616

M3 - Article

SN - 0167-8019

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EP - 143

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 2

ER -

On the Wiener semigroup and harmonic analysis on the infinite dimensional torus

Abstract

Keywords

ASJC Scopus subject areas

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