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\(L^p\)-independence of spectral radius for generalized Feynman–Kac semigroups

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Abstract

Under mild conditions on measures used in the perturbation, we establish the \(L^p\)-independence of spectral radius for generalized Feynman–Kac semigroups without assuming the irreducibility and the boundedness of the function appeared in the continuous additive functionals locally of zero energy in the framework of symmetric Markov processes. These results are obtained by using the gaugeability approach developed by the first named author as well as the recent progress on the irreducible decomposition for Markov processes proved by the third author and on the analytic characterizations of gaugeability for generalized Feynman–Kac functionals developed by the second and third authors.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto, 860-8555, Japan

    Daehong Kim

  3. Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka, 814-0180, Japan

    Kazuhiro Kuwae

Authors
  1. Zhen-Qing Chen
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  2. Daehong Kim
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  3. Kazuhiro Kuwae
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Corresponding author

Correspondence to Kazuhiro Kuwae.

Additional information

Communicated by Y. Giga.

The research of the first named author is partially supported by Simons Foundation Grant 520542 and a Victor Klee Faculty Fellowship at UW. The second named author was partially supported by a Grant-in-Aid for Scientific Research (C) No. 17K05304 from Japan Society for the Promotion of Science. The third named author was partially supported by a Grant-in-Aid for Scientific Research (B) No. 17H02846 from Japan Society for the Promotion of Science.

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Chen, ZQ., Kim, D. & Kuwae, K. \(L^p\)-independence of spectral radius for generalized Feynman–Kac semigroups. Math. Ann. 374, 601–652 (2019). https://doi.org/10.1007/s00208-018-1746-0

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  • DOI: https://doi.org/10.1007/s00208-018-1746-0

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