Criteria for analyticity of subordinate semigroups. (English) Zbl 1162.47036
Summary: Let \(\psi\) be a Bernstein function. A.S.Carasso and T.Kato [Trans.Am.Math.Soc.327, No.2, 867–878 (1991; Zbl 0743.47017)] obtained necessary and sufficient conditions for \(\psi\) to have the property that \(\psi (A)\) generates a quasibounded holomorphic semigroup for every generator \(A\) of a bounded \(C_{0}\)-semigroup in a Banach space, in terms of some convolution semigroup of measures associated with \(\psi\). We give an alternative to Carasso–Kato’s criterion, and derive several sufficient conditions for \(\psi\) to have the above mentioned property.
MSC:
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47A60 | Functional calculus for linear operators |
Keywords:
strong continuity; holomorphic semigroup; subordination; functional calculus; operator functionCitations:
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