Boundary Theory for Symmetric Markov Processes

This chapter proposes a boundary theory for symmetric Markov processes. It begins by investigating the relationship between the space (Fₑ,E) and the space ((ℱ⁰)ref, ℰ 0,ref). Next, the chapter focuses on the restricted spaces ℱ₀∣F, ℱ∣F and their descriptions in terms of the Feller measures U, V, and U α‎ and the Douglas integrals defined by them. The chapter then introduces the lateral condition for the L² generator and studies the case where the set F consists of countably many points that are located in an invariant way under a quasi-homeomorphism. It then turns to one-point extensions and examples of these, and follows up with many-point extensions and their examples as well.