Subordination in the sense of Bochner and a related functional calculus
René L. Schilling · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1998
Abstract We prove a new representation of the generator of a subordinate semigroup as limit of bounded operators. Our construction yields, in particular, a characterization of the domain of the generator. The generator of a subordinate semigroup can be viewed as a function of the generator of the original semigroup. For a large class these functions we show that operations at the level of functions has its counterpart at the level of operators.