A characterization of the inverse Radon transform associated with the classical domain of type one

作者：Li, Yafeng^*; Feng, Xiangchu; He, Jianxun

来源：Integral Transforms and Special Functions, 2009, 20(8): 569-579.

DOI：10.1080/10652460902723580

• radon transform
• continuous wavelet transform
• classical domain of type one
• Siegel domain
• nilpotent Lie group of step two
• Heisenberg group

Let D(Omega, Phi) be the unbounded realization of the classical domain D(I) of type one. In general, its Silov boundary N is a nilpotent Lie group of step two. In this article, we characterize a subspace S(R)(N) of S(N) (Schwartz space) on which the Radon transform is a bijection and give another characterization S*, 2(N) for this subspace SR(N). Also, we show that the two characterizations are equivalent. Finally, we give an inversion formula of the Radon transform on N by using continuous wavelet transform.

• 出版日期2009
• 单位广州大学; 西安电子科技大学