Measure Perturbations of Markovian Semigroups

摘要

The perturbation of the semigroup of a Borel right process by a class of signed measures on the state space of the process in studies. The perturbation is defined by a Feynman-Kac functional associated with the measure. Under appropriate conditions the perturbed semigroup is strongly continuous in L~p(m), 1 <= p < infinity where m is a fixed excessive measure. Both existence and uniqueness of the associated Schrodinger type equation are investigated.