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We consider the Radon transform R , ␣ G 0, on the Laguerre hypergroup ␣ w w Ks 0, qϱ ‫.ޒ=‬ We characterize a space of infinitely differentiable and rapidly decreasing functions together with their derivatives such that R is a bijection ␣ 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 Wiener-Tauberian theorem is proven on the Laguerre hypergroup [M.M. Nessibi, K. Trimèche, Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets, J. Math. Anal. Appl. 208 (1997) 337-363]. As consequence of this theorem we establish a Pompeiu type-theorem and we study some of its applications.

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