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.
- AMS subject classifications: 35RJ20, 60B15, 60G30
- Infinite-dimensional analysis
- Wiener measure
- partial differential equations
ASJC Scopus subject areas
- Applied Mathematics