Examples

Abstract

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 ⁺.