An Inversion Formula Of Radon Transform And Weyl Transform On The Product Heisenberg Group

Let H1 be the real 3-diemensional Heisenberg group, then we call Hn1 = H1×H1×...×H1 the product Heisenberg group. In this article, we first discuss thegeneralized wavelet transform of the product Heisenberg group, and use the inversewavelet transform to get an inversion formula of Radon transform. In addition, westudy the boundedness of Weyl transform associated with the wavelet transform. Itconsists of 3 chapters:In Chapter 1, the academic background is introduced.In Chapter 2, we study the Fourier transform defined by Schro¨dinger representa-tions and construct the wavelet transform on the product Heisenberg group. Moreover,we obtain an inversion formula of Radon transform by using the inverse wavelet trans-form.In Chapter 3, we study the Fourier transform related to the Bargmann-Fock rep-resentations and the wavelet transform on the product Heisenberg group. Furthermore,we investigate the boundedness of Weyl transform associated with the wavelet trans-form.