A counterexample to the conjecture: Let $S$ be a singular inner function. Then $z\cdot S$ is onto $U$

TL;DR

This paper provides a counterexample to a conjecture in complex analysis, showing that for a singular inner function S, the multiplication by z does not necessarily map onto the entire space U.

Contribution

The paper introduces a specific counterexample disproving the conjecture about singular inner functions and their multiplication properties.

Findings

Counterexample demonstrates the conjecture is false.

Shows that z·S is not always onto U for singular inner functions.

Challenges previous assumptions in the theory of inner functions.

Abstract

In this paper we give a counterexample to the conjecture: Let $S\in{\rm SInn}$. Then $z\cdot S$ is onto $U$.