# Weighted integral Hankel operators with continuous spectrum

## TL;DR

This paper characterizes the absolutely continuous spectrum of a class of weighted integral Hankel operators in L^2(R+), extending previous unweighted cases and employing the Kato-Rosenblum theorem for spectral analysis.

## Contribution

It extends the spectral analysis of Hankel operators to weighted cases with continuous spectrum, generalizing prior unweighted results and providing a broader understanding of their spectral properties.

## Key findings

- Describes the absolutely continuous spectrum of weighted Hankel operators
- Extends unweighted case analysis to weighted operators with parameter alpha
- Employs Kato-Rosenblum theorem for spectral characterization

## Abstract

Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in $L^2(\mathbb R_+)$. These self-adjoint operators generalise the explicitly diagonalisable operator with the integral kernel $s^\alpha t^\alpha(s+t)^{-1-2\alpha}$, where $\alpha>-1/2$. Our analysis can be considered as an extension of J.Howland's 1992 paper which dealt with the unweighted case, corresponding to $\alpha=0$.