Potential theory for Green functions of Schrödinger-type operators
Volume 250 / 2020
Studia Mathematica 250 (2020), 109-127
MSC: Primary 60J45; Secondary 31C25, 60J25.
DOI: 10.4064/sm171220-6-11
Published online: 5 July 2019
Abstract
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.
