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


In this chapter we present examples of Dirichlet forms. We try to keep close to situations very likely to be encountered in applications, i.e., we consider in the respective sections, cases where one of the following is given: 1. some linear operator; 2. some bilinear form on finite or 3. infinite dimensional state space; 4. a semigroup of kernels; 5. a resolvent of kernels. In each case we show under what conditions and how to obtain the corresponding Dirichlet form. In this chapter for E we shall take various topological spaces. If we do not specify the σ-algebra B explicitly, it is understood to be the corresponding Borel-σ-algebra B(E). We denote by B b , B+ the bounded respectively positive B-measurable functions on E and set B b + := B b B + .


Bilinear Form Dirichlet Form Finite Dimensional Case Positive Radon Measure Schwartz Distribution 
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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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