Additive functionals and perturbation of semigroup (Q5955020)

Starting with a Borel right Markov process on a Lusin space, a few switching identities and formulae concerning dual additive functionals and Revuz measures are first given. The perturbation of the transition semigroup by a non-necessarily continuous additive functional is next considered. The main result of the paper shows that Kato type conditions on the additive functional are sufficient to ensure the strong continuity of the perturbed semigroup on \(L^{p}\)-spaces (\(1\leq p \leq +\infty \)). Such results were obtained by \textit{R. K. Getoor} [Potential Anal. 11, No. 2, 101-133 (1999; Zbl 0945.60062)], for the perturbation of the transition semigroup by continuous additive functionals. A final paragraph is devoted to the study of the existence and uniqueness for the corresponding Schrödinger equation.