A characterization of inverse Radon transform on the Laguerre hypergroup

作者：He; JX

来源：Journal of Mathematical Analysis and Applications, 2006, 318(1): 387-395.

DOI：10.1016/j.jmaa.2005.05.069

• radon transform
• wavelet transform
• Laguerre hypergroup

Let K = [0, infinity) x R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this note we give another characterization for a subspace of S(K) (Schwartz space) such that the Radon transform R-alpha on K is a bijection. We show that this characterization is equivalent to that in [M.M. Nessibi, K. Trimeche, Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets, J. Math. Anal. Appl. 208 (1997) 337-363]. In addition, we establish an inversion formula of the Radon transform R,, in the weak, sense.

• 出版日期2006-6-1
• 单位广州大学