GENERALIZED WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP

摘要

Let X = R_+~n x R denote the underlying manifold of polyradial functions on the Heisenberg group H_n. We construct a generalized translation on X = R_+~n x R, and establish the Plancherel formula on L~2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L~2(X,d/μ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.