On a family of integral operators of Hankel type

TL;DR

This paper explicitly diagonalizes a family of Hankel integral operators, revealing that each has a simple, purely absolutely continuous spectrum spanning the interval [-1,1], extending previous results in the field.

Contribution

The paper provides an explicit diagonalization of Hankel integral operators, generalizing earlier spectral results to a broader family of such operators.

Findings

Each operator has a purely absolutely continuous spectrum.

The spectrum fills the entire interval [-1,1].

The results extend previous spectral analyses of Hankel operators.

Abstract

In this paper we perform an explicit diagonalization of Hankel integral operators $ K^{(0)}, K^{(1)}, K^{(2)}, ... $ It turns out that each of these operators has a simple purely absolutely continuous spectrum filling in the interval $ [-1,1] $. This generalizes a result of Kostrykin and Makarov (2008).