Potential theory for Green functions of Schrödinger-type operators

Masayoshi Takeda Studia Mathematica MSC: Primary 60J45; Secondary 31C25, 60J25. DOI: 10.4064/sm171220-6-11 Opublikowany online: 5 July 2019


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.


  • Masayoshi TakedaDepartment of Mathematics
    Faculty of Engineering Science
    Kansai University
    3-3-35 Yamate-cho, Suita-shi
    Osaka 564-8680, Japan

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