Dirichlet Spaces and Strong Markov Processes
Open Access
- 1 December 1971
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 162, 185-224
- https://doi.org/10.2307/1995748
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.Keywords
This publication has 10 references indexed in Scilit:
- Markov Processes and Potential Theory. By R. M. Blumenthal and R. K. Getoor. Pp. x, 313. £7. 1968. (Academic Press.)The Mathematical Gazette, 1972
- Regular Representations of Dirichlet SpacesTransactions of the American Mathematical Society, 1971
- On Dirichlet spaces and Dirichlet ringsProceedings of the Japan Academy, Series A, Mathematical Sciences, 1969
- Probability and PotentialsMathematics of Computation, 1967
- Processus de MarkovLecture Notes in Mathematics, 1967
- Applications to analysis of a topological definition of smallness of a setBulletin of the American Mathematical Society, 1966
- Algebraic Criterion on Quasiconformal Equivalence of Riemann SurfacesNagoya Mathematical Journal, 1960
- Resolvents, Transition Functions, and Strongly Markovian ProcessesAnnals of Mathematics, 1959
- DIRICHLET SPACESProceedings of the National Academy of Sciences, 1959
- Les espaces du type de Beppo LeviAnnales de l'institut Fourier, 1954