Weighted integral Hankel operators with continuous spectrum
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Publication:6282740
DOI10.1515/CONOP-2017-0009zbMath1517.47046arXiv1702.00636MaRDI QIDQ6282740
Alexander Pushnitski, Emilio Fedele
Publication date: 2 February 2017
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 $s^alpha t^alpha(s+t)^{-1-2alpha}$, 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 $alpha=0$.
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