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Keywords:
sub-Markovian semigroup; potential; Bochner subordination; exit law; $\mathcal{C}^{1}$-subordinator; one-sided stable subordinator
sub-Markovian semigroup; potential; Bochner subordination; exit law; $\mathcal{C}^{1}$-subordinator; one-sided stable subordinator
Summary:
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.
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