Subordination in the sense of Bochner
and a related functional calculus

René L. Schilling
Max-Planck-Institut
Für Mathematik in den Naturwissenschaften
Inselstrasse 22-26
04103 Leipzig
Germany

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.

PDF file size:

© Copyright 1998, Australian Mathematical Society