One-component inner functions

Abstract

We explicitely unveil several classes of inner functions $u$ in $H^{\infty }$ with the property that there is $\eta \in ]0,1[$ such that the level set ${\Omega }_u(\eta ):=\{z\in \mathbb{D}:|u(z)|<\eta \}$ is connected. These so-called one-component inner functions play an important role in operator theory.

16 pages, 2 figures