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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)

43A62 Harmonic analysis on hypergroups
44A12 Radon transform
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