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Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets. (English) Zbl 0870.43004
From the authors’ abstract: We consider the Radon transform $$R_\alpha$$, $$\alpha\geq 0$$, on the Laguerre hypergroup $$K=[0,+\infty[\times\mathbb{R}$$. 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 $$R_\alpha$$.
Reviewer: N.Bozhinov (Sofia)

MSC:
 43A62 Harmonic analysis on hypergroups 44A12 Radon transform
Full Text:
References:
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