On Dirichlet forms and semi-Dirichlet forms

Abstract

One aim of this note is to give an overview of some developments in the area of Dirichlet forms. A second aim is to review the new book "Semi-{D}irichlet forms and {M}arkov processes" by Yoichi Oshima. The book appeared last year, but first versions were written as lecture notes 25 years ago. We first give a rather short and light introduction into the field of Dirichlet forms with a special emphasis on the subjects presented in the book under consideration. After a small account on the history of Dirichlet forms we comment on the book by Oshima against the background of related works.