@article{Asharabi2024, 
author = {Rashad M. Asharabi and Somaia M. Alhazmi},
title = {Accelerating the convergence of a two-dimensional periodic nonuniform sampling series through the incorporation of a bivariate Gaussian multiplier},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30898-30921},
keywords = {two-dimensional periodic nonuniform sampling, sinc approximation, Gaussian regularization, entire functions of exponential type, error bounds},
url = {https://www.sciopen.com/article/10.3934/math.20241491},
doi = {10.3934/math.20241491},
abstract = {Recently, in the field of periodic nonuniform sampling, researchers (Wang et al., 2019; Asharabi, 2023) have investigated the incorporation of a Gaussian multiplier in the one-dimensional series to improve its convergence rate. Building on these developments, this paper aimed to accelerate the convergence of the two-dimensional periodic nonuniform sampling series by incorporating a bivariate Gaussian multiplier. This approach utilized a complex-analytic technique and is applicable to a wide range of functions. Specifically, it applies to the class of bivariate entire functions of exponential type that satisfy a decay condition, as well as to the class of bivariate analytic functions defined on a bivariate horizontal strip. The original convergence rate of the two-dimensional periodic nonuniform sampling is given by  O(N−p), where  p≥1. However, through the implementation of this acceleration technique, the convergence rate improved drastically and followed an exponential order, specifically  e−αN, where  α>0. To validate the theoretical analysis presented, the paper conducted rigorous numerical experiments.}
}