On the Range of the Radon Transform on Zn and the Related Volberg’s Uncertainty Principle

Abstract

We characterize the image of exponential type functions under the discrete Radon transform R on the lattice Zn of the Euclidean space Rn n≥2. We also establish the generalization of Volberg's uncertainty principle on Zn, which is proved by means of this characterization. The techniques of which we make use essentially in this paper are those of the Diophantine integral geometry as well as the Fourier analysis.