Weighted integral Hankel operators with continuous spectrum

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 \(\alpha=0\).