Heisenberg 群上的逆Radon变换.doc

  Heisenberg 群上的逆Radon变换 钟晓红1，何建勋2 1 2 广州大学数学与信息科学学院，广州　510006 广州大学数学与信息科学学院，广州　510006 摘要：在本文中我们引入了和Heisenberg群上的对合相联系的酉算子，其不变闭子空间就是 次Laplace算子的特征子空间. 在向量值意义下讨论了连续小波变换的理论,给出了Radon变换 的逆公式. 关键词：对合; 小波变换; Radon变换; Heisenberg群 中图分类号： O174.2 Inverse Radon Transforms on the Heisenberg Group Zhong Xiao-Hong 1, He Jian-Xun2 1 2 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006 Abstract: In this article, we introduce a kind of unitary operator U associated with the involution on the Heisenberg group, invariant closed subspaces are identi?ed with the characterization spaces of sub-Laplacian operators. In the sense of vector-valued functions, we study the theory of continuous wavelet transform. Also, we obtain a new inversion formula of Radon transform on the Heisenberg group Hn. Key words: involution; wavelet transform; Radon transform; Heisenberg group  0  Introduction  The research of Radon transform has made considerable progress due to its wide applica- tions to partial di?erential equations, X-ray technology, radio astronomy and so on. The basic theory and some new developments can be found in [1] by Helgason and the references therein. The combination of Radon transform and wavelet transform has proved to be very useful both in pure mathematics and applied subjects. Recently, a lot of authors deal with the inversion formula of the Radon transform by using the inverse wavelet transforms. The ?rst result in this area is due to Holschneider who considered the classical Radon transform on the two- dimensional plane (see [2]). His result was extended by Rubin (see [3, 4]) to the k-dimensional Radon transform on Rn and totally geodesic Radon transforms on the sphere and the hyper- bolic space. Strichartz [5] investigated the theory of the Radon transform on the Heisenberg group. Nessibi and Trim`eche [6] gave an inversion formula of the Radon