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Subordination in the sense of Bochner and a related functional calculus
Part of
René L. Schilling
Journal:

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 64 / Issue 3 / June 1998

Published online by Cambridge University Press:

09 April 2009, pp. 368-396

Print publication:

June 1998
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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.

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Subordination in the sense of Bochner and a related functional calculus