If $(e^{-tA})_{t>0}$ is a strongly continuous and contractive semigroup on a complex Banach space $B$, then $-(-A)^\alpha $, $0<\alpha <1$, generates a holomorphic semigroup on $B$. This was proved by K. Yosida in [7]. Using similar techniques, we present a class $H$ of Bernstein functions such that for all $f\in H$, the operator $-f(-A)$ generates a holomorphic semigroup.
@article{119334,
author = {Adel Saddi},
title = {Holomorphic subordinated semigroups},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {457-466},
zbl = {1090.35109},
mrnumber = {1920520},
language = {en},
url = {http://dml.mathdoc.fr/item/119334}
}
Saddi, Adel. Holomorphic subordinated semigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 457-466. http://gdmltest.u-ga.fr/item/119334/
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