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A class of singular integral operators, encompassing two physically relevantcases arising in perturbative QCD and in classical fluid dynamics, is presentedand analyzed. It is shown that three special values of the parameters allow foran exact eigenfunction expansion; these can be associated to Riemanniansymmetric spaces of rank one with positive, negative or vanishing curvature.For all other cases an accurate semiclassical approximation is derived, basedon the identification of the operators with a peculiar Schroedinger-likeoperator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory