Dirichlet spaces on H-convex sets in Wiener space

Details Dirichlet spaces on H-convex sets in Wiener space Dirichlet spaces on H-convex sets in Wiener space

2011-05-17

arxiv.org/abs/1105.3300v1

Mathematics

Probability

17 pages, 1 figure

Scientific paper

We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an
abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$.
We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset
if $U$ is $H$-convex and $H$-open. For the proof, the relations between
$H$-notions and quasi-notions are also studied.

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