We consider a second-order singular di erential operator L on the half line which generalizes the Bessel operator. We construct a pair transmutation operators between L and the second derivative opera- tor d2=dx2. Using these transmutation operators, we rstly establish a Paley-Wiener theorem for the Fourier transform associated to L, and secondly introduce a generalized convolution on [0,∞[ tied to L. Fur- thermore, a generalization of the classical Sonine integral transform is built.