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Transactions of the American Mathematical Society

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Analytic characterizations of gaugeability for generalized Feynman-Kac functionals


Authors: Daehong Kim and Kazuhiro Kuwae
Journal: Trans. Amer. Math. Soc. 369 (2017), 4545-4596
MSC (2010): Primary 31C25, 60J45, 60J57; Secondary 35J10, 60J35, 60J25
DOI: https://doi.org/10.1090/tran/6702
Published electronically: November 16, 2016
MathSciNet review: 3632543
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Abstract: We give analytic characterizations of gaugeability for generalized Feynman-Kac functionals including continuous additive functional of zero quadratic variation in the framework of symmetric Markov processes. Our result improves the previous work on the analytic characterization due to Z.-Q. Chen (2003) even if we restrict ourselves to deal with non-local perturbations. We also prove that such a characterization is also equivalent to semi-conditional gaugeability and to the subcriticality of the Schrödinger operator associated to our generalized Feynman-Kac semigroup under the conditional (semi-)Green-tightness of related measures.


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Additional Information

Daehong Kim
Affiliation: Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto, 860-8555 Japan
Email: daehong@gpo.kumamoto-u.ac.jp

Kazuhiro Kuwae
Affiliation: Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto, 860-8555 Japan
Address at time of publication: Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka, 814-0180 Japan
Email: kuwae@gpo.kumamoto-u.ac.jp, kuwae@fukuoka-u.ac.jp

DOI: https://doi.org/10.1090/tran/6702
Keywords: Feynman-Kac semigroup, symmetric Markov processes, Dirichlet forms, irreducibility, absolute continuity condition, continuous additive functional of zero energy, Kato class, extended Kato class, Green-boundedness, Green-tight measures of Kato class, semi-Green-tight measures of extended Kato class, Green-tight measures of Kato class in the sense of Chen, semi-Green-tight measures of extended Kato class in the sense of Chen, conditional Green-boundedess, conditionally Green-tight measures in the sense of Chen, conditionally Green-bounded jump functions, conditionally Green-tight jump functions
Received by editor(s): October 15, 2012
Received by editor(s) in revised form: December 26, 2013, February 17, 2014, and July 6, 2015
Published electronically: November 16, 2016
Additional Notes: The first named author was partially supported by a Grant-in-Aid for Scientific Research (C) No. 23540147 from Japan Society for the Promotion of Science
The second named author was partially supported by a Grant-in-Aid for Scientific Research (B) No. 22340036 from Japan Society for the Promotion of Science
Article copyright: © Copyright 2016 American Mathematical Society

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