A new representation of Hankel operators and its spectral consequences

TL;DR

This paper introduces a novel way to represent Hankel operators as pseudo-differential operators with special structured amplitudes, leading to new insights into their spectral properties.

Contribution

It presents a new representation of Hankel operators as pseudo-differential operators with structured amplitudes, revealing spectral implications.

Findings

Spectral analysis of compact Hankel operators is enhanced.

Operators with continuous spectrum are better understood.

New representation simplifies spectral computations.

Abstract

We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of functions of a one variable only. This representation has numerous spectral consequences both for compact Hankel operators and for operators with the continuous spectrum.