On multidimensional sinc-Gauss sampling formulas for analytic functions. ETNA - Electronic Transactions on Numerical Analysis
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7 janvier 2022
- handle: 10670/1.9q20xz
- issn: 1068-9613
- doi: 10.1553/etna_vol55s242
info:eu-repo/semantics/openAccess
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Felwah H. Al-Haddad et al., « On multidimensional sinc-Gauss sampling formulas for analytic functions. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol55s242
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Résumé
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.