Inner functions and inner factors of their derivatives

TL;DR

This paper investigates the properties of derivatives of inner functions with derivatives in the Nevanlinna class, focusing on their canonical inner-outer factorizations.

Contribution

It explores the inner-outer factorization of derivatives of inner functions whose derivatives belong to the Nevanlinna class, addressing several open problems.

Findings

Characterization of the inner factors of derivatives

Conditions for the existence of canonical factorizations

Connections between inner functions and their derivatives' factorization

Abstract

For an inner function $\theta$ with $\theta'\in\mathcal N$, where $\mathcal N$ is the Nevanlinna class, several problems are posed in connection with the canonical (inner-outer) factorization of $\theta'$.