Potential theory for Green functions of Schrödinger-type operators
A potential theory for Green kernels of Schrödinger-type operators is considered. We give a condition for the Green kernel to satisfy Ugaheri’s maximum principle in terms of the bottom of the spectrum of the time-changed process. The condition also leads to the continuity principle. For the proofs, we use probabilistic arguments, in particular, the strong Markov property and strong Feller property.