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arXiv · 0908.1607

The uniqueness of symmetrizing measure and linear diffusions

Xing Fang·Jiangang Ying·Minzhi Zhao
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Abstract

In this short article, we shall study one-dimensional local Dirichlet spaces. One result, which has its independent interest, is to prove that irreducibility implies the uniqueness of symmetrizing measure for right Markov processes. The other result is to give a representation for any 1-dim local, irreducible and regular Dirichlet space and a necessary and sufficient condition for a Dirichlet space to be regular subspace of another Dirichlet space.

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Xing Fang, Jiangang Ying, Minzhi Zhao. 2009-08-12. The uniqueness of symmetrizing measure and linear diffusions. https://arxiv.org/abs/0908.1607

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