A commutator method for the diagonalization of Hankel operators

TL;DR

This paper introduces a commutator-based method for explicitly diagonalizing certain Hankel operators, recovering classical results and deriving new findings through their commutation with second-order differential operators.

Contribution

The paper presents a novel commutator approach that enables explicit diagonalization of Hankel operators, expanding understanding of their spectral properties.

Findings

Recovered classical diagonalization results for Hankel operators

Derived new spectral results using the commutator method

Established a link between Hankel operators and differential operators

Abstract

We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new results. Our approach relies on the commutation of a Hankel operator with some differential operator of second order.