Measures and Dirichlet forms under the Gelfand transform

2012/12/05 by Michael Hinz, Hinz, Michael, Daniel Kelleher +3
Mathematics · #28A25 #31C25 #46E25 #54E45 #60J25 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Probability (math.PR) #math.FA #math.GN #math.PR #msc:28A25 #msc:31C25 #msc:46E25 #msc:54E45 #msc:60J25

paper · pdf · doi:10.48550/arxiv.1212.1099

arxiv created 2013/08/01 · arxiv updated 2013/08/02

Abstract

Using the standard tools of Daniell-Stone integrals, Stone-Čech 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-Čech 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.

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