Criteria for analyticity of subordinate semigroups

Abstract

Let ψ be a Bernstein function. A. Carasso and T. Kato obtained necessary and sufficient conditions for ψ to have a property that ψ(A) generates a quasibounded holomorphic semigroup for every generator A of a bounded C0-semigroup in a Banach space, in terms of some convolution semigroup of measures associated with ψ. We give an alternative to Carasso-Kato’s criterium, and derive several sufficient conditions for ψ to have the above-mentioned property.