Generators of semigroups on Banach spaces inducing holomorphic semiflows

Abstract

Let $A$ be the generator of a $C_0$-semigroup $T$ on a Banach space of analytic functions on the open unit disc. If $T$ consists of composition operators, then there exists a holomorphic function $G:\mathbb{D}\to \mathbb{C}$ such that $Af=G{f}^{\prime }$ with maximal domain. The aim of the paper is the study of the reciprocal implication.

14 pages, Accepted, Israel Journal of Mathematics 2018