The Nehari problem for the Paley--Wiener space of a disc

TL;DR

This paper investigates the Nehari problem within the Paley--Wiener space of a disc, revealing the existence of bounded Hankel operators that cannot be represented by bounded symbols.

Contribution

It demonstrates that not all bounded Hankel operators on the Paley--Wiener space of a disc are generated by bounded symbols, highlighting a nuanced aspect of the Nehari problem.

Findings

Existence of bounded Hankel operators without bounded symbols

Counterexample to the classical Nehari problem in this setting

Insights into the structure of operators on the Paley--Wiener space

Abstract

There is a bounded Hankel operator on the Paley--Wiener space of a disc in $\mathbb{R}^2$ which does not arise from a bounded symbol.