Semigroups of Composition Operators on Hardy Spaces of the half-plane

TL;DR

This paper characterizes semigroups of bounded composition operators on Hardy spaces of the upper half-plane, showing their strong continuity, lack of uniform continuity, and identifying their infinitesimal generators.

Contribution

It provides a complete characterization of semigroups of bounded composition operators on Hardy spaces of the upper half-plane, including their continuity properties and generators.

Findings

Semigroups are strongly continuous but not uniformly continuous on $H^p()$.

The infinitesimal generators of these semigroups are explicitly identified.

The paper advances understanding of operator semigroups in complex analysis contexts.

Abstract

We identify the semigroups consisting of bounded composition operators on the Hardy spaces $H^p(\U)$ of the upper half-plane. We show that any such semigroup is strongly continuous on $H^p(\U)$ but not uniformly continuous and we identify the infinitesimal generator.