Abstract
In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations (see Definition 1.2), we give a necessary and sufficient condition on the stability of global two-sided (upper) estimates for fundamental solution of Feynman–Kac semigroup of X. As a corollary, under the same assumptions, a weak type of global two-sided (upper) estimates holds for the fundamental solution of Feynman–Kac semigroup with (extended) Kato class conditions for measures. This generalizes all known results on the stability of global integral kernel estimates by symmetric Feynman–Kac perturbations with Kato class conditions in the framework of symmetric Markov processes.
Funding Statement
The first named author was supported in part by JSPS Grant-in-Aid for Scientific Research (KAKENHI) 20K03635. The second named author was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1E1A1A01941893). The third named author was supported in part by JSPS Grant-in-Aid for Scientific Research (KAKENHI) 17H02846 and by fund (No. 185001) from the Central Research Institute of Fukuoka University.
Citation
Daehong KIM. Panki KIM. Kazuhiro KUWAE. "Stability of estimates for fundamental solutions under Feynman–Kac perturbations for symmetric Markov processes." J. Math. Soc. Japan 75 (2) 527 - 572, April, 2023. https://doi.org/10.2969/jmsj/88038803
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