Analytic characterizations of gaugeability for generalized Feynman-Kac functionals

Kim, Daehong; Kuwae, Kazuhiro

doi:10.1090/tran/6702

Analytic characterizations of gaugeability for generalized Feynman-Kac functionals
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by Daehong Kim and Kazuhiro Kuwae PDF

Trans. Amer. Math. Soc. 369 (2017), 4545-4596 Request permission

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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