ABSTRACT
In this chapter it is shown that the bridge between Gauss’s and Shannon’s work is constituted by certain extensions of the famous Hardy–Landau identities in geometric lattice point theory. Particular interest is laid on the matter dealing with bandlimited functions corresponding to, e.g., geoscientifically relevant regions (cf. W. Freeden, M.Z. Nashed [2015]). The routes to sampling expansions are exhibited in Paley-Wiener spaces, leading to multivariate sinc-type reproducing kernels and spline integration formulas over regular regions.
