## On multidimensional sinc-Gauss sampling formulas for analytic functions

### Abstract

Using complex analysis, we present new error estimates for multidimensional sinc-Gauss sampling formulas for multivariate analytic functions and their partial derivatives, which are valid for wide classes of functions. The first class consists of all $n$-variate entire functions of exponential type satisfying a decay condition, while the second is the class of $n$-variate analytic functions defined on a multidimensional horizontal strip. We show that the approximation error decays exponentially with respect to the localization parameter $N$. This work extends former results of the first author and J. Prestin, [IMA J. Numer. Anal., 36 (2016), pp. 851–871] and [Numer. Algorithms, 86 (2021), pp. 1421–1441], on two-dimensional sinc-Gauss sampling formulas to the general multidimensional case. Some numerical experiments are presented to confirm the theoretical analysis.

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### Key words

multidimensional sinc-Gauss sampling formula, multivariate analytic function, localization operator, error estimate

### AMS subject classifications

94A20, 32A15, 41A25, 41A80

### Links to the cited ETNA articles

 [5] Vol. 52 (2020), pp. 320-341 Rashad M. Asharabi and Fatemah M. Al-Abbas: Error analysis for regularized multidimensional sampling expansions

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