Univalent functions in model spaces: revisited

TL;DR

This paper investigates conditions under which certain model subspaces of the Hardy space contain bounded univalent functions, motivated by approximation theory problems.

Contribution

It provides a necessary and sufficient condition for model subspaces to contain bounded univalent functions, advancing understanding in function theory.

Findings

Characterization of model subspaces containing bounded univalent functions

Necessary and sufficient condition derived

Implications for approximation theory

Abstract

Motivated by a problem in approximation theory, we find a necessary and sufficient condition for a model (backward shift invariant) subspace $K_\varTheta = H^2\ominus \varTheta H^2$ of the Hardy space $H^2$ to contain a bounded univalent function.