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A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables

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Abstract

Recently, Norvidas has introduced the general multidimensional Hermite sampling series, which involves samples from a function and its mixed and non-mixed partial derivatives. The convergence of this sampling series is slow unless the sample values |f(x)| rapidly decay as \(|x_j| \rightarrow \infty \) for all \(1 \le j \le n\). In this paper, we investigate a modified version of this sampling series that utilizes a multivariate Gaussian multiplier to approximate functions from two classes of multivariate analytic functions using a complex approach. The first class comprises entire functions of exponential type in n variables that fulfill a decay condition, while the second class includes analytic functions in n variables defined on a multidimensional horizontal strip. It has a significantly higher convergence rate compared to the general multidimensional Hermite sampling series.

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Acknowledgements

The authors thank the referees for their constructive comments

Funding

The authors are thankful to the Deanship of Scientific Research at Najran University for funding this work, under the Distinguished Research Funding program grant code NU/DRP/SERC /12/7

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Authors and Affiliations

  1. Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia

    Rashad M. Asharabi & Felwah H. Al-Haddad

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  1. Rashad M. Asharabi
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  2. Felwah H. Al-Haddad
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The authors contributed equally and they read and approved the final manuscript for publication

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Correspondence to Rashad M. Asharabi.

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Asharabi, R.M., Al-Haddad, F.H. A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables. Numer Algor 96, 105–134 (2024). https://doi.org/10.1007/s11075-023-01641-7

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