Killing transform on regular Dirichlet subspaces

TL;DR

This paper investigates how killing transforms affect regular Dirichlet subspaces, revealing that the large jump component of the Dirichlet form is not crucial for their analysis, which simplifies understanding their structure.

Contribution

It demonstrates that the big jump part of a Dirichlet form is non-essential for the study of its regular Dirichlet subspaces using killing transforms.

Findings

Big jump part is not essential for regular Dirichlet subspaces

Killing transform preserves key properties of subspaces

Simplifies analysis of Dirichlet forms

Abstract

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 [6].