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Transactions of the American Mathematical Society

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



Regular representations of Dirichlet spaces

Author: Masatoshi Fukushima
Journal: Trans. Amer. Math. Soc. 155 (1971), 455-473
MSC: Primary 60.60
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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Keywords: <IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$D$">-space, underlying space, <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="${L^2}$">-resolvent, regular <IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="$D$">-space, Ray resolvent, strongly regular <IMG WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$D$">-space, Ray process, regular representation, continuous embedding
Article copyright: © Copyright 1971 American Mathematical Society