## Adel Saddi

*Holomorphic subordinated semigroups *

Comment.Math.Univ.Carolinae 43,3 (2002) 457-466. **Abstract:**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.

**Keywords:** holomorphic semigroup, Bernstein function

**AMS Subject Classification:** 35K65, 35B65, 35B40

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