Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in L2(ℝ+). These self-adjoint operators generalise the explicitly diagonalisable operator with the integral kernel sαtα(s + t)-1-2α, where α > -1/2. Our analysis can be considered as an extension of J. Howland’s 1992 paper which dealt with the unweighted case, corresponding to α = 0.
@article{bwmeta1.element.doi-10_1515_conop-2017-0009,
author = {Emilio Fedele and Alexander Pushnitski},
title = {Weighted integral Hankel operators with continuous spectrum},
journal = {Concrete Operators},
volume = {4},
year = {2017},
pages = {121-129},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2017-0009}
}
Emilio Fedele; Alexander Pushnitski. Weighted integral Hankel operators with continuous spectrum. Concrete Operators, Tome 4 (2017) pp. 121-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2017-0009/