Semigroups of weighted composition operators on spaces of holomorphic functions

TL;DR

This paper introduces properties of semigroups of weighted composition operators acting on spaces of holomorphic functions, highlighting their mathematical structure and potential applications.

Contribution

It provides an introductory analysis of discrete and continuous $C_0$-semigroups of (weighted) composition operators on analytic function spaces.

Findings

Characterization of $C_0$-semigroups of composition operators

Analysis of weighted composition operators on various spaces

Insights into the structure and properties of these semigroups

Abstract

This paper is based on three hours of lectures given by the first author in the "Focus Program on Analytic Function Spaces and their Applications" July 1 -- December 31, 2021, organized by the Fields Institute for Research in Mathematical Sciences. The goal of this paper is to give an introduction to the properties of discrete and continuous $C_0$-semigroups of (weighted) composition operators on various spaces of analytic functions.