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Regularization

  • Zhi-Ming Ma
  • Michael Röckner
Part of the Universitext book series (UTX)

Abstract

In this chapter we present a general “local compactification” method that enables us to associate to a quasi-regular Dirichlet form on an arbitrary topological space a regular Dirichlet form on a locally compact separable metric space. This is done in such a way that we can transfer results obtained in the latter “classical” framework to our more general situation. The “local compactification” is constructed in Section 1 and it is shown that “without loss of generality” one can also restrict to Hunt processes. In Section 2 the “transfer method” is described in general and subsequently illustrated by several examples. In all of this chapter E is supposed to be a Hausdorff topological space with B(E) = σ(C(E)). We fix a σ-finite positive measure m on (E, B(E)) and a quasi-regular Dirichlet form (ε, D(ε)) on L2(E; m).

Keywords

Dirichlet Form Transfer Method Trivial Extension Local Compactification Hausdorff Topological Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Zhi-Ming Ma
    • 1
  • Michael Röckner
    • 2
  1. 1.Institute of Applied MathematicsAcademia SinicaBeijingPeople’s Republic of China
  2. 2.Institut für Angewandte MathematikUniversität BonnBonn 1Germany

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