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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
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