A variational formula for Dirichlet forms and existence of ground states

摘要

Let L be the generator of a symmetric Markov process on a locally compact separable metric space, and μ a certain measure in the Kato class. Employing a variational formula for Dirichlet forms, we show the existence of a ground state of the time-changed operator — 1/μ L or the Schr?dinger-type operator — L + μ.