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Some Results on Energy

  • Zoran R. Pop-Stojanovic
  • Murali Rao
Chapter
  • 270 Downloads
Part of the Progress in Probability and Statistics book series (PRPR, volume 1)

Abstract

The concept of energy we are dealing with here is a generalization of that dealt with in the classical theory. Although rightfully observed by P.A. Meyer in [4] p. 140, that such a generalization “loses delicacy as it gains generality”, we will try to add a few results which may somewhat simplify a way in dealing with this concept. To be more precise, in the literature dealing with concept of energy, the basic tools are Dirichlet spaces techniques [7] and the kernel theory, which are both natural offshoots of the classical theory. The symmetry of kernels plays the basic role there.

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References

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    R.M. BLUMENTHAL and R.K. GETOOR. Markov Processes and Potential Theory, Academic Press, New York, 1968.Google Scholar
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    H. CARTAN. Théorie du potential newtoniani énergie, capacité, suites de potentials. Bull. Soc. Math. France 73, 74–106 (1945).Google Scholar
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    L.L. HELMS. Introduction to Potential Theory. Wiley-Interscience, New York, 1969.Google Scholar
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    P.A. MEYER. Probability and Potentials. Blaisdell, Waltham, 1966.Google Scholar
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    C. DELLACHERIE and P.A. MEYER. Probabilités et Potentiel, Vol. II. Hermann, Paris, 1980.Google Scholar
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    M.L. SILVERSTEIN. The sector condition implies that semipolar sets are quasi-polar. Z. Wahrscheinlichkeitstheorie verw. Gebiete 41 (1977), 13–33.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1981

Authors and Affiliations

  • Zoran R. Pop-Stojanovic
    • 1
  • Murali Rao
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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