Killing Transform on Regular Dirichlet Subspaces

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• 作者：Liping Li ; Jiangang Ying
• 关键词：Dirichlet form ; Regular Dirichlet subspace ; Killing transform ; Resurrected transform ; Multiplicative functional
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：46
• 期：1
• 页码：105-118
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Potential Theory; Probability Theory and Stochastic Processes; Geometry; Functional Analysis;
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：46

文摘

In this paper, we shall consider the killing transform induced by a multiplicative functional on regular Dirichlet subspaces of a fixed Dirichlet form. Roughly speaking, a regular Dirichlet subspace is a closed subspace with Dirichlet and regular properties of fixed Dirichlet space. By using the killing transforms, our main results indicate that the big jump part of fixed Dirichlet form is not essential for discussing its regular Dirichlet subspaces. This fact is very similar to the status of killing measure when we consider the questions about regular Dirichlet subspaces in Li-and-Ying (2015).