Stability of estimates for fundamental solutions under Feynman–Kac perturbations for symmetric Markov processes

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  • Kim Daehong
    Faculty of Advanced Science and Technology, Kumamoto University
  • Kim Panki
    Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University
  • Kuwae Kazuhiro
    Department of Applied Mathematics, Fukuoka University

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<p>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.</p>

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