Part of the Mathematics and Its Applications book series (MAIA, volume 253)
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Dirichlet forms are various generalizations of the classical Dirichlet integral
where Ω is a domain in ℝn, f∈C 0 ∞ (ℝn). The relation between the above Dirichlet integral, the solution of the Dirichlet problem for the Laplacian on Ω, “stopped” Brownian motion, and the associated heat equation (and its semigroup) has long been known. We refer to Fukushima (1980) and Silverstein (1974) for systematic, self-contained expositions, and for comprehensive references.
KeywordsHilbert Space Energy Form Radon Measure Dirichlet Form Selfadjoint Operator
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© Springer Science+Business Media Dordrecht 1993