A sufficient condition for the Carasso-Kato theorem
\textit{A. S. Carasso} and \textit{T. Kato} [Trans. Am. Math. Soc. 327, No. 2, 867-878 (1991; Zbl 0743.47017)] exhibited a large class of probability measures such that the subordinated semigroups are always holomorphic. In addition they obtained a necessary condition on the measure's Laplace transform for that to be the case. In the present paper, when the exponent is regularly varying, we give a sufficient condition for that to be the case. Several examples are given to illustrate this sufficient condition.
scientific article; zbMATH DE number 537353