Time changes of local Dirichlet spaces by energy measures of harmonic functions

Given a (symmetric) recurrent local regular Dirichlet form with state space E and an associated symmetric diffusion {X-t}(t is an element of)[0,infinity) on E, we consider a function h which belongs to the extended Dirichlet space, is harmonic outside F-1 boolean OR F-2 and equal to a on F-1 and to b on F-2, where F-1. F-2 subset of E are (epsilon-quasi-)closed sets and a, b is an element of R, a < b. We prove that the time change of the real-valued process {h(X-t)}(t is an element of)[0,infinity) by the energy measure mu((h)) of h is a reflecting Brownian motion on [a, b]. As an application, we also discuss asymptotic analysis of the heat kernel on the harmonic Sierpinski gasket.