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Russian Mathematical Surveys, 1972, Volume 27, Issue 1, Pages 43–84
DOI: https://doi.org/10.1070/RM1972v027n01ABEH001363
(Mi rm5006)
 

This article is cited in 14 scientific papers (total in 15 papers)

Integral representation of exctssive measures and excessive functions

E. B. Dynkin
References:
Abstract: One of the central results of classical potential theory is the theorem on the representation of an arbitrary non-negative superharmonic function in the form of a sum of a Green's potential and a Poisson integral. We obtain similar integral representations for the excessive measures and functions connected with an arbitrary Markov transition function. Many authors have studied the homogeneous excessive measures connected with a homogeneous transition function. We begin with the inhomogeneous case and then reduce the homogeneous case to it. The method proposed gives a considerable gain in generality.
The investigation is carried out in the language of convex measurable spaces and in contrast to previous papers no topological arguments are used. Our basis are the results obtained in (also without topology) on the integral representation of Markov processes with a given transition function. For the reduction of the homogeneous case to the inhomogeneous we use a theorem from the theory of dynamical systems due to Yu. I. Kifer and S. A. Pirogov (see the Appendix at the end of this paper).
Received: 18.10.1971
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: English
Original paper language: Russian
Citation: E. B. Dynkin, “Integral representation of exctssive measures and excessive functions”, Russian Math. Surveys, 27:1 (1972), 43–84
Citation in format AMSBIB
\Bibitem{Dyn72}
\by E.~B.~Dynkin
\paper Integral representation of exctssive measures and excessive functions
\jour Russian Math. Surveys
\yr 1972
\vol 27
\issue 1
\pages 43--84
\mathnet{http://mi.mathnet.ru//eng/rm5006}
\crossref{https://doi.org/10.1070/RM1972v027n01ABEH001363}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=405602}
\zmath{https://zbmath.org/?q=an:0321.60002}
Linking options:
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  • https://doi.org/10.1070/RM1972v027n01ABEH001363
  • https://www.mathnet.ru/eng/rm/v27/i1/p43
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:463
    Russian version PDF:155
    English version PDF:27
    References:93
    First page:3
     
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