On the Wiener semigroup and harmonic analysis on the infinite dimensional torus
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.
scientific article; zbMATH DE number 4073628