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Holomorphic subordinated semigroups. (English) Zbl 1090.35109
Summary: 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. 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.

##### MSC:
 35K65 Degenerate parabolic equations 35B65 Smoothness and regularity of solutions to PDEs 35B40 Asymptotic behavior of solutions to PDEs
##### Keywords:
holomorphic semigroup; Bernstein function
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