Abstract:We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on $L^2(m)$. We mainly investigate subordinated semigroups in the Bochner sense by means of $\mathcal{C}^{1}$-subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.
Keywords: sub-Markovian semigroup, potential, Bochner subordination, exit law, $\mathcal{C}^{1}$-subordinator, one-sided stable subordinator
AMS Subject Classification: 4703 31C15 39B42 60J99