On Laguerre Superior Generalized Wavelet Transform And The Radon Transform Inverse Formula

M. M. Nessibi and K. Trimeche studied the theory of generalized wavelet transform on the underlying manifold of square integrable radial functions space on the Heisen-berg group Hn. They constructed an inversion formula of the Radon transform on the underlying manifold by means of generalized wavelet. In this paper, we deal with the analogous problems of square integrable polyradial functions space on Hn.In chapter one, we present some basic concepts and fundamental results about wavelet transform in common sense.In chapter two, we first give the condition of generalized wavelets on L2(X) by using the Gelfand transform, where X = R+R denotes the underlying manifold of square integrable polyradial functions on the Heisenberg group Hn. Then, we establish the theory of generalized wavelet transform and generalized wavelet packet transform on it.In chapter three, as an application of the theory of generalized wavelet transform, we obtain an inversion formula of the Radon transform on X .