Measure Perturbations of Markovian Semigroups

The perturbation of the semigroup of a Borel right process by a class of signed measures on the state space of the process is studied. 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< where m is a fixed excessive measure. Both existence and uniqueness of the associated Schrödinger type equation are investigated.