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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 408, Pages 303–322 (Mi znsl5507)  
This article is cited in 12 scientific papers (total in 12 papers)

Measures and Dirichlet forms under the Gelfand transform

M. Hinzab, D. Kellehera, A. Teplyaeva

a Department of Mathematics, University of Connecticut, Storrs, CT, USA
b Mathematisches Institut, Friedrich-Schiller-Universität Jena, Germany
Full-text PDF (276 kB) Citations (12)
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Abstract: 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.
Key words and phrases: regular symmetric Dirichlet form, $C^*$-algebra, Daniell–Stone integral, Stone–Čech compactification, Gelfand transform, fractals.
Received: 15.10.2012
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 199, Issue 2, Pages 236–246
DOI: https://doi.org/10.1007/s10958-014-1851-x
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: English
Citation: M. Hinz, D. Kelleher, A. Teplyaev, “Measures and Dirichlet forms under the Gelfand transform”, Probability and statistics. Part 18, Zap. Nauchn. Sem. POMI, 408, POMI, St. Petersburg, 2012, 303–322; J. Math. Sci. (N. Y.), 199:2 (2014), 236–246
Citation in format AMSBIB
\Bibitem{HinKelTep12}
\by M.~Hinz, D.~Kelleher, A.~Teplyaev
\paper Measures and Dirichlet forms under the Gelfand transform
\inbook Probability and statistics. Part~18
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 408
\pages 303--322
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5507}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3032223}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 2
\pages 236--246
\crossref{https://doi.org/10.1007/s10958-014-1851-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902264061}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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