正则Dirichlet形式的正则子空间

正则Dirichlet形式的正则子空间问题,即存在性及其刻画等问题,是作者关注近20年的问题,该问题来自第二作者对于Markov过程的Killing变换的Dirichlet形式刻画问题的研究,这个问题是Dirichlet形式理论的一个基本问题,在最近10年中取得了一点进展.本文将主要叙述问题及其背景,并介绍围绕该问题得到的一些结果与遗留的问题.

Regular subspaces of regular Dirichlet forms

This paper focuses on the problem of the existence and representation of regular Dirichlet subspaces of a regular Dirichlet form,which was raised by the second author when studying the characterization of Killing transform of Markov processes by Dirichlet forms,and has been studied for about 20 years.A brief survey on recent progress on this problem in the frame of 1-dimensional symmetric di?usions is presented.