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Subordination in the sense of Bochner and a related functional calculus

Part of: General theory of linear operators Groups and semigroups of linear operators, their generalizations and applications Markov processes

Published online by Cambridge University Press:  09 April 2009

René L. Schilling
René L. Schilling
Affiliation:
Max-Planck-InstitutFür Mathematik in den Naturwissenschaften Inselstrasse 22-26 04103 LeipzigGermany
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Abstract

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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.

Keywords

strongly continuous semigroupsubordinationfunctional calculusfunctions of an operator.

MSC classification

Secondary: 47D03: Groups and semigroups of linear operators 47A60: Functional calculus 60J35: Transition functions, generators and resolvents
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 3 , June 1998 , pp. 368 - 396
Copyright
Copyright © Australian Mathematical Society 1998

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