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
Issue number2
StatePublished - Oct 1987


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

ASJC Scopus subject areas

  • Applied Mathematics


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