Journal of Mathematical Sciences

, Volume 199, Issue 2, pp 236–246 | Cite as

Measures and Dirichlet Forms Under the Gelfand Transform


Using the standard tools of Daniell–Stone integrals, Stone–Čech compactification, and Gelfand transform, we show explicitly that any closed 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. Bibliography: 29 titles.


Radon Energy Measure Dirichlet Form Riesz Representation Theorem Stone Property 


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Friedrich-Schiller-UniversitätJenaGermany
  2. 2.University of ConnecticutStorrsUSA

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