On subordinated holomorphic semigroups
Authors:
Alfred S. Carasso and Tosio Kato
Journal:
Trans. Amer. Math. Soc. 327 (1991), 867878
MSC:
Primary 47D03; Secondary 60J35
MathSciNet review:
1018572
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Abstract 
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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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 K. Yosida, An abstract analyticity in time for solutions of a diffusion equation, Proc. Japan Acad. 35 (1959), 109113. MR 0105559 (21:4298)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199110185724
PII:
S 00029947(1991)10185724
Keywords:
Subordinated semigroups,
holomorphic extensions
Article copyright:
© Copyright 1991 American Mathematical Society
