Unbounded Hankel operators and the flow of the cubic Szeg\H{o} equation

TL;DR

This paper demonstrates that Hankel operators with symbols in Hardy space have coinciding maximal and minimal domains, enabling the continuous extension of the cubic Szeg\

Contribution

It establishes the domain equivalence for Hankel operators with Hardy class symbols and extends the cubic Szeg\

Findings

Domains of Hankel operators with Hardy symbols coincide.

Flow of the cubic Szeg\

Continuous extension of the flow to all of H^2.

Abstract

We prove that, for any Hankel operator with a symbol from the Hardy class $H^2$, the maximal and minimal domains coincide. As an application, we prove that the evolution flow of the cubic Szeg\H{o} equation on the unit circle can be continuously extended to the whole class $H^2$.