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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 R 2 and analytic functions on a bivariate strip. The first modification is given for the twodimensional 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.

Abstract. We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

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