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Journal of the Australian Mathematical Society - Series A
Vol. 64 Part 3 (1998)

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.

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© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
1998-09-18