Measure perturbations of Markovian semigroups (Q1304704)

The paper contains the (close to) ultimate result on (signed) measure perturbations of generators of strongly continuous Markovian semigroups. No symmetry assumptions are needed. The paper makes use of advanced (but widely used) Markov process theory. Though the main tool is still the Feynman-Kac functional, a number of refinements in comparison with previous approaches are necessary such as e.g. defining generalized Kato classes in this non-symmetric set-up. Two sections are devoted to proving existence and uniqueness of solutions to the associated Schrödinger type equations after defining an appropriate notion of solution in this general situation.