Abstract
Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in $L^2(\bbR_+)$. 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 $\alpha=0$.
Original language | English |
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Pages (from-to) | 121–129 |
Journal | Concrete Operators |
Volume | 4 |
Issue number | 1 |
Early online date | 31 Oct 2017 |
DOIs | |
Publication status | Published - Oct 2017 |
Keywords
- Weighted Hankel operators
- Absolutely continuous spectrum