Multi-variate Hardy-type lattice point summation and Shannon-type sampling (Q901330)

This work is concerned with multi-variate Hardy-type lattice point identities and their connections with the state-dependent Shannon sampling (S. s.) theorem. This (S. s.) theorem investigates how a signal band-limited to a regular region in a \(q\)-dimensional Euclidean space allows a reconstruction from discrete values in the lattice points of a (general) \(q\)-dimensional lattice. It should be noted that classical theory deals with discrete signals and we can capture essential information about the underlying continuous phenomenon. In this paper, the authors made the attempt to work out their interrelations.