Abstract
We study criticalities of generalized Schrödinger operators in terms of the Schrödinger forms induced by generalized Feynman-Kac perturbations of symmetric Markov processes, which extend earlier work due to Takeda [26]. The related functional inequalities and analytic characterizations of criticalities of Schrödinger forms are given. As applications, we establish some maximum principles via the analytic characterization.
Funding Statement
The first named author was partially supported by a Grant-in-Aid for Scientific Research (C) No. 17K05304 from Japan Society for the Promotion of Science.
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The second named author was partially supported by a Grant-in-Aid for Scientific Research (B) No. 17H02846 from Japan Society for the Promotion of Science.
Citation
Daehong Kim. Kazuhiro Kuwae. "Generalized Schrödinger forms with applications to maximum principles." Osaka J. Math. 58 (3) 731 - 753, July 2021.
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