Effective intervals and regular Dirichlet subspaces
Abstract
It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in the representation above. Finally applying previous results, we shall prove that every regular and local Dirichlet form has a special standard core generated by a continuous and strictly increasing function.
Cite
@article{arxiv.1805.09499,
title = {Effective intervals and regular Dirichlet subspaces},
author = {Liping Li and Wenjie Sun and Jiangang Ying},
journal= {arXiv preprint arXiv:1805.09499},
year = {2018}
}