Dirichlet spaces on H-convex sets in Wiener space
Masanori Hino

TL;DR
This paper studies the structure of Sobolev spaces on H-convex subsets of Wiener space, establishing density of smooth cylindrical functions under certain convexity and openness conditions.
Contribution
It proves that the Sobolev space W^{1,2}(U) has smooth cylindrical functions dense when U is H-convex and H-open, linking H- and quasi-notions.
Findings
Density of smooth cylindrical functions in W^{1,2}(U) for H-convex, H-open sets
Relations between H- and quasi-notions in Wiener space
Enhanced understanding of Dirichlet spaces on convex subsets
Abstract
We consider the -Sobolev space on subsets in an abstract Wiener space, which is regarded as a canonical Dirichlet space on . We prove that has smooth cylindrical functions as a dense subset if is -convex and -open. For the proof, the relations between -notions and quasi-notions are also studied.
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