Measures and Dirichlet forms under the Gelfand transform
Functional Analysis
2013-08-02 v2 General Topology
Probability
Abstract
Using the standard tools of Daniell-Stone integrals, Stone-\v{C}ech compactification and Gelfand transform, we discuss how any Dirichlet form defined on a measurable space can be transformed into a regular Dirichlet form on a locally compact space. This implies existence, on the Stone-\v{C}ech compactification, of the associated Hunt process. As an application, we show that for any separable resistance form in the sense of Kigami there exists an associated Markov process.
Cite
@article{arxiv.1212.1099,
title = {Measures and Dirichlet forms under the Gelfand transform},
author = {Michael Hinz and Daniel Kelleher and Alexander Teplyaev},
journal= {arXiv preprint arXiv:1212.1099},
year = {2013}
}