多重Fourier变换与Hankel变换的关系

The relation between multiple Fourier transforms and Hankel transforms

本文利用多重付立叶（Ｆｏｕｒｉｅｒ）变换证明亨克尔（Ｈａｎｋｅｌ）变换的反演定理，同时，把Ｋ维空间的射线函数（仅依赖于到原点距离的函数）的付立叶变换，归结为一维空间的亨克尔交换，这样，由Ｋ元函数的付立叶交换成立的定理，就可推出一元函数的亨克尔变换相应的定理．

In this peper, we prove the inversion theory of Hankel transforms by using of multiple Fourier transforms, and in the meantime we can use the Fourier transforms of ray function in k -dimensional Spacs, sum up to the Hankel transforms of one-dimensional Space, thus by the Fourier transforms theory of k-variable function we can get the corresponding theory of Hankel transforms on one-variable function.