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Mathematische Annalen

, Volume 374, Issue 1–2, pp 601–652 | Cite as

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

  • Zhen-Qing Chen
  • Daehong Kim
  • Kazuhiro KuwaeEmail author
Article

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.

Mathematics Subject Classification

Primary 31C25 60J45 60J57 Secondary 35J10 60J35 60J25 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Mathematics and Engineering, Graduate School of Science and TechnologyKumamoto UniversityKumamotoJapan
  3. 3.Department of Applied Mathematics, Faculty of ScienceFukuoka UniversityFukuokaJapan

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