Analyticity of semigroups on the right half-plane

TL;DR

This paper investigates the extension properties of semigroups of composition operators and holomorphic mappings on the right half-plane, linking their extendability to the geometry of associated domains and the properties of their generators.

Contribution

It provides new conditions for extending semigroups in sectors based on generator properties and characterizes composition operators on Hardy spaces of the right half-plane.

Findings

Extension sectors depend on generator image properties

Complete characterization of composition operators on Hardy spaces

Size of extension sector controlled by domain geometry

Abstract

This paper is devoted to the study of semigroups of composition operators and semigroups of holomorphic mappings. We establish conditions under which these semigroups can be extended in their parameter to sector given a priori. We show that the size of this sector can be controlled by the image properties of the infinitesimal generator, or, equivalently, by the geometry of the so-called associated planar domain. We also give a complete characterization of all composition operators acting on the Hardy space $H^p$ on the right half-plane.