Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 490601, 7 pages
Research Article

The Radon Transforms on the Generalized Heisenberg Group

1School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China

Received 5 September 2013; Accepted 7 October 2013; Published 2 January 2014

Academic Editors: R. Curto and D.-X. Zhou

Copyright © 2014 Tianwu Liu and Jianxun He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be the generalized Heisenberg group. In this paper, we study the inversion of the Radon transforms on . Several kinds of inversion Radon transform formulas are established. One is obtained from the Euclidean Fourier transform; the other is derived from the differential operator with respect to the center variable . Also by using sub-Laplacian and generalized sub-Laplacian we deduce an inversion formula of the Radon transform on .