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Transactions of the American Mathematical Society

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Regular representations of Dirichlet spaces


Author: Masatoshi Fukushima
Journal: Trans. Amer. Math. Soc. 155 (1971), 455-473
MSC: Primary 60.60
DOI: https://doi.org/10.1090/S0002-9947-1971-0281256-1
MathSciNet review: 0281256
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Abstract: We construct a regular and a strongly regular Dirichlet space which are equivalent to a given Dirichlet space in the sense that their associated function algebras are isomorphic and isometric. There is an appropriate strong Markov process called a Ray process on the underlying space of each strongly regular Dirichlet space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0281256-1
Keywords: $ D$-space, underlying space, $ {L^2}$-resolvent, regular $ D$-space, Ray resolvent, strongly regular $ D$-space, Ray process, regular representation, continuous embedding
Article copyright: © Copyright 1971 American Mathematical Society