On two-dimensional classical and Hermite sampling

We investigate some modifications of the two-dimensional sampling series with a Gaussian function for wider classes of bandlimited functions, including unbounded entire functions on ℝ² and analytic functions on a bivariate strip. The first modification is given for the two-dimensional version of the Whittaker-Kotelnikov-Shannon sampling (classical sampling), and the second is given for two-dimensional sampling involving values of all partial derivatives of order α ≤ 2 (Hermite sampling). These modifications improve the convergence rate of classical and Hermite sampling which will be of exponential type. Numerical examples are given to illustrate the advantages of the new method.