On regular Dirichlet subspaces of $H^{1}(I)$ and associated linear diffusions

Abstract

We will give a complete characterization of all regular Dirichlet subspaces of $H^1(I)$ for a finite open interval $I$ by a certain family of scale functions. Each associated diffusion will be constructed from a reflecting Brownian motion on a closed interval by a time change and a transformation of the state space.