62
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Inversion of the Radon transform on the product Laguerre hypergroup by using generalized wavelets

&
Pages 287-295 | Received 14 Jun 2006, Accepted 04 Jan 2007, Published online: 17 May 2007
 

Abstract

Let H 1 be the three-dimensional Heisenberg group. The fundamental manifold of the radial function space for H 1 can be denoted by [0, ∞)×R, which is just the Laguerre hypergroup. Naturally, K n =[0, ∞) n ×R n is the product Laguerre hypergroup. In this paper, we give the theory of continuous wavelet analysis and the Radon transform on K n , and devise a subspace 𝒮(K n ) of 𝒮(K n ) (Schwartz space) on which the Radon transform is a bijection. Also, we give two equivalent characterizations on 𝒮(K n ) for the Radon transform. By using the inverse wavelet transform we establish an inversion formula of the Radon transform on K n in the weak sense.

Acknowledgements

The authors would like to thank the referee for his/her valuable comments on this paper. J. He is supported by the National Natural Science Foundation of China (No. 10371087, 10671041), the Science Research Foundation of Guangzhou Educational Bureau.

Additional information

Notes on contributors

Pei Liu

Email: [email protected]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.