On the Range of the Radon Transform onZnand the Related Volberg’s Uncertainty Principle

We characterize the image of exponential type functions under the discrete Radon transformRon the latticeZnof the Euclidean spaceRn n≥2. We also establish the generalization of Volberg's uncertainty principle onZn, 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.