On the Königs function of semigroups of holomorphic self-maps of the unit disc

Abstract

Let $({\varphi }_t)$ be a semigroup of holomorphic self-maps of~$\mathbb{D}$. In this note, we use an abstract approach to define the Königs function of $({\varphi }_t)$ and "holomorphic models" and show how to deduce the existence and properties of the infinitesimal generator of $({\varphi }_t)$ from this construction.

arXiv comment16 pages