Inverse Radon Transform And The Calder(?)n Reproducing Formula Associated With The Heisenberg Group

This paper is concerned with inverse Radon transform and the convergence ofCalder(?)n reproducing formula in Lp(Hn)(1<p <∞). It consists of3chapters.In Chapter1, the academic background, the theories of Fourier transform andwavelet transform in L2(R), classic Radon transform are introduced.In Chapter2, we study Fourier transform defined by Bargmann-Fock represen-tation and construct the wavelet transform on the Heisenberg group. Furthermore,a kind of unitary operator associated with the involution on the Heisenberg group isdefined, invariant closed subspaces in L2(Hn) are identified with the characterizationspaces of sub-Laplacian operators. In the sense of vector-valued functions, we studythe theory of continuous wavelet transform. Also, we obtain a new inversion formulaof Radon transform on the Heisenberg group Hn.In Chapter3, combined with the properties of Heisenberg group, we establishthe convergence of the Calder(?)n reproducing formula in L2norm on the Heisen-berg group Hn. Furthermore, a reconstruction wavelet is defined, we investigate theCalder(?)n reproducing formula in Lp(Hn) for any1<p <∞is convergent and in thea.e. sense.