On multidimensional sinc-Gauss sampling formulas for analytic functions

Electronic Transactions on Numerical Analysis

article

Rashad M. Asharabi¹  Felwah H. Al-Haddad¹ 

[1] Department of Mathematics, College of Arts and Sciences, Najran University

关键词: multidimensional sinc-Gauss sampling formula;    multivariate analytic function;    localization operator;    error estimate;   

DOI  :  10.1553/etna_vol55s242

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

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.

【 授权许可】

Unknown