A sufficient condition for the Carasso-Kato theorem (Q1318170)
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scientific article; zbMATH DE number 537353
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sufficient condition for the Carasso-Kato theorem |
scientific article; zbMATH DE number 537353 |
Statements
A sufficient condition for the Carasso-Kato theorem (English)
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13 July 1994
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\textit{A. S. Carasso} and \textit{T. Kato} [Trans. Am. Math. Soc. 327, No. 2, 867-878 (1991; Zbl 0743.47017)] exhibited a large class of probability measures such that the subordinated semigroups are always holomorphic. In addition they obtained a necessary condition on the measure's Laplace transform for that to be the case. In the present paper, when the exponent is regularly varying, we give a sufficient condition for that to be the case. Several examples are given to illustrate this sufficient condition.
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probability measures
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subordinated semigroups
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Laplace transform
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