On Dirichlet forms and semi-Dirichlet forms

TL;DR

This paper reviews recent developments in Dirichlet and semi-Dirichlet forms, highlighting the contributions of Yoichi Oshima's book and providing a concise introduction to the field's history and key concepts.

Contribution

It offers an overview of Dirichlet forms, reviews Oshima's book on semi-Dirichlet forms, and contextualizes these within the broader research landscape.

Findings

Summarizes key developments in Dirichlet forms

Provides insights into Oshima's book and its significance

Highlights historical context and evolution of the field

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.