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On Subordinated Holomorphic Semigroups

1991
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Transactions of the American Mathematical Society
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If [e~' ] is a uniformly bounded C0 semigroup on a complex Banach space X, then -A" , 0 < a < 1, generates a holomorphic semigroup on X , and [e ] is subordinated to [e ] through the Levy 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

doi:10.2307/2001827
fatcat:mcovrth7kfbuxcuqe65fdx7ehe