| 概要 | In the first part of this talk, I will present a useful criterion for
uniform integrability of exponential martingales in the context of
Markov processes. The condition of this criterion is easy to verify
and is, in general, much weaker than the commonly used Novikov's
condition. In the second part of this talk, I will present a new
approach to the study of spectral bounds of Feynman-Kac semigroups
for a large class of symmetric Markov processes. Criteria for the
$L^p$-independence of spectral bounds for Feynman-Kac semigroups
generated by continuous additive functionals will be derived, using
gaugeability results for Schrodinger operators. These analytic
criteria are then extended to non-local Feynman-Kac semigroups via
pure jump Girsanov transforms. For this, the uniform integrability
result of the exponential martingales plays an important role. |