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