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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Dirichlet spaces and strong Markov processes

Author: Masatoshi Fukushima
Journal: Trans. Amer. Math. Soc. 162 (1971), 185-224
MSC: Primary 60J45
MathSciNet review: 0295435
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Abstract: We show that there exists a suitable strong Markov process on the underlying space of each regular Dirichlet space. Potential theoretic concepts due to A. Beurling and J. Deny are then described in terms of the associated strong Markov process. The proof is carried out by developing potential theory for Dirichlet spaces and symmetric Ray processes and by using a method of transformation of underlying spaces.

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Keywords: Capacity, regular Dirichlet space, quasi-continuity, equilibrium potential, quasi-homeomorphism, Ray process, Hunt process, fine continuity, hitting probability, reference measure
Article copyright: © Copyright 1971 American Mathematical Society