Geodesic
On exit laws for subordinated semigroups by means of $\cal{C}^{1}$-subordinators
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 4, pp. 605-617.

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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.
Classification : 31C15, 39B42, 47D03, 60J99
Keywords: sub-Markovian semigroup; potential; Bochner subordination; exit law; $\mathcal{C}^{1}$-subordinator; one-sided stable subordinator 
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Hmissi, Mohamed; Mliki, Ezzedine. On exit laws for subordinated semigroups by means of $\cal{C}^{1}$-subordinators. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 4, pp. 605-617. http://geodesic.mathdoc.fr/item/CMUC_2010__51_4_a5/