A new representation of Hankel operators and its spectral consequences

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.

Dedicated to the memory of Mikhail Zakharovich Solomyak