On subordinated holomorphic semigroups

Authors:
Alfred S. Carasso and Tosio Kato

Journal:
Trans. Amer. Math. Soc. **327** (1991), 867-878

MSC:
Primary 47D03; Secondary 60J35

DOI:
https://doi.org/10.1090/S0002-9947-1991-1018572-4

MathSciNet review:
1018572

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Abstract: If is a uniformly bounded semigroup on a complex Banach space , then , , generates a holomorphic semigroup on , and is subordinated to through the Lévy stable density function. This was proved by Yosida in 1960, by suitably deforming the contour in an inverse Laplace transform representation. Using other methods, we exhibit a large class of probability measures such that the subordinated semigroups are always holomorphic, and obtain a necessary condition on the measure's Laplace transform for that to be the case. We then construct probability measures that do not have this property.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-1018572-4

Keywords:
Subordinated semigroups,
holomorphic extensions

Article copyright:
© Copyright 1991
American Mathematical Society