Inversion of the Radon Transform on the Laguerre Hypergroup by using Generalized Wavelets

We consider the Radon transform R , a G0, on the Laguerre hypergroup a Ksw0,q`w=R. We characterize a space of infinitely differentiable and rapidly decreasing functions together with their derivatives such that R is a bijection a from this space onto itself. We establish an inversion formula and a Plancherel theorem for the operator R . Finally, by using the continuous wavelet transform a on the Laguerre hypergroup K, we deduce another expression for the inverse Ry1 a of the operator Ra .