乘积拉盖尔超群上的Radon变换及其反演

摘要

The inversion Radon transform on the product Laguerre hypergroup Kn is discussed. At first, the the-ory of continuous wavelet analysis on Kn is given, then the Plancherel theory and Parseval formula on Kn are ob-tained. Furthermore,the expression of Radon transform on Kn is provided. At last, using the generalized wavelet transform the inversion formula of Radon transform on Kn is established.%主要讨论乘积Laguerre超群Kn上的Radon反演公式.首先定义Kn上的广义平移算子,其次研究Kn上的广义Fourier变换,得到Kn上的Plancherel定理及Parseval等式.在此基础上,给出Kn上Radon变换具体表达式.最后利用广义小波变换得到Radon变换的反演公式.