The Formula Of Inverse Radon Transform On The Quaternion Heisenberg Group

Let H_q~nbe the (4n+3) dimensional quaternion Heisenberg group. This paper isconcerned with inverse Radon transform on H_q~n. It consists of3Chapters. First, weintroduce the academic background the harmonic analysis on H_q~n. Then we give thedirect sum decomposition for L~2(H_q~n) in terms of the group Fourier transform and westudy the sublaplacian L on H_q~n. We discuss the properties of the admissible waveletson H_q~nassociated with L, we also construct a class of radial wavelets.Moreover, combining the group Fourier transform and L on H_q~n, we research theRadon transform, and we make use of the wavelets to derive an inversion formula ofthe Radon transform.