Inversion of the radon transform on the Laguerre hypergroup by using generalized wavelets

[摘要] We consider the Radon transform R-alpha, alpha greater than or equal to 0, on the Laguerre hypergroup K = [0, +infinity[x R. We characterize a space of infinitely differentiable and rapidly decreasing functions together with their derivatives such that R-alpha is a bijection from this space onto itself. We establish an inversion formula and a Plancherel theorem for the operator R-alpha. Finally, by using the continuous wavelet transform on the Laguerre hypergroup K, we deduce another expression for the inverse R-alpha(-1) of the operator R-alpha. (C) 1997 Academic Press.

[发布日期] 1997-04-15