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Inversion of the Radon Transform on the Laguerre Hypergroup by using Generalized Wavelets

✍ Scribed by M.M. Nessibi; K. Trimèche

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
337 KB
Volume
208
Category
Article
ISSN
0022-247X

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✦ Synopsis

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 ␣ on the Laguerre hypergroup K, we deduce another expression for the inverse R y1 ␣ of the operator R .

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