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- W4239421331 abstract "If $[{e^{ - tA}}]$ is a uniformly bounded ${C_0}$ semigroup on a complex Banach space $X$, then $- {A^alpha },$, $0 < alpha < 1$, generates a holomorphic semigroup on $X$, and $[{e^{ - t{A^alpha }}}]$ is subordinated to $[{e^{ - tA}}]$ 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 measureâs Laplace transform for that to be the case. We then construct probability measures that do not have this property." @default.
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- W4239421331 date "1991-10-01" @default.
- W4239421331 modified "2023-09-26" @default.
- W4239421331 title "On Subordinated Holomorphic Semigroups" @default.
- W4239421331 doi "https://doi.org/10.2307/2001827" @default.
- W4239421331 hasPublicationYear "1991" @default.
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