Slice regular composition operators

TL;DR

This paper introduces a globally defined regular composition for slice regular functions, enabling the development of a comprehensive theory of composition operators and dynamical systems, including classical results like Littlewood's principle and Denjoy-Wolff theorem.

Contribution

It presents a new globally defined regular composition for slice regular functions, expanding the theoretical framework and applications in dynamical systems and operator theory.

Findings

The new composition is globally defined, unlike Vlacci's local version.

Established a Littlewood subordination principle for slice regular functions.

Proved a Denjoy-Wolff type theorem in this context.

Abstract

In the article the class of slice regular functions is shown to be closed under a new regular composition. The new regular composition turns out to be globally defined in contrast to the locally defined version by Vlacci. Its advantage over Vlacci's is demonstrated by its associated theory of composition operators and dynamical systems for slice regular functions. Especially, the corresponding Littlewood subordination principle and the Denjoy-Wolff type theorem can be established.