A Wiener–Tauberian and a Pompeiu type theorems on the Laguerre hypergroup

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.