Dynamics for affine composition operators on weighted Bergman space of a half plane

TL;DR

This paper characterizes the dynamics of affine composition operators on weighted Bergman spaces of the right half-plane, focusing on properties like positivity, expansiveness, and shadowing.

Contribution

It provides a complete characterization of positive expansive and Cesàro composition operators induced by affine self-maps on the weighted Bergman space of the half-plane.

Findings

Characterization of positive expansive composition operators

Identification of operators with the positive shadowing property

Complete description of affine composition operators on the space

Abstract

In this article, we completely characterize the positive expansive and absolutely Ces\`aro composition operators $C_{\phi}f=f\circ \phi$ induced by affine self-maps $\phi$ of the right half-plane $\mathbb{C}_+$ on the weighted Bergman space $\mathcal{A}^2_{\alpha}(\mathbb{C}_+)$. Furthermore, we characterize which of these operators have the positive shadowing property.