# Criteria for analyticity of subordinate semigroups

## TL;DR

This paper provides new criteria and sufficient conditions for Bernstein functions to ensure that the associated operator generates a quasibounded holomorphic semigroup, extending previous work by Carasso and Kato.

## Contribution

It offers an alternative to Carasso-Kato's criteria and introduces several new sufficient conditions for Bernstein functions to generate holomorphic semigroups.

## Key findings

- Derived alternative criteria for Bernstein functions to generate holomorphic semigroups.
- Established several new sufficient conditions for these functions.
- Extended the theoretical understanding of semigroup generation in Banach spaces.

## Abstract

Let $\psi$ be a Bernstein function. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $\psi$ to have a 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 criterium, and derive several sufficient conditions for $\psi$ to have the above-mentioned property.