HOLOMORPHIC EXTENSION OF CERTAIN DISCRETE FUNCTIONS ON Z(n) AND THE RELATED PROBLEMS

摘要

In this paper, we construct an holomorphic extension of certain functions on Z(n). We deduce a discrete Gutzmer's formula for the discrete Fourier transform (see Theorem 4.4). In addition, we prove the Hardy-Littlewood inequality for the classical Radon transform on R-n (see Theorem 4.7). In this work, we use the techniques of the diophantine integral geometry and the estimate method in certain weighted L-2-spaces.