C&SA | Contents

Volume 61 >>> № 1 JANUARY — FEBRUARY 2025

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DOI 10.34229/KCA2522-9664.25.1.14

UDC 519.8

I.V. Kal’chuk¹, Y.V. Pryvalov²

¹ Lesya Ukrainka Volyn National University, Lutsk, Ukraine

k.inna.80@gmail.com

² Lesya Ukrainka Volyn National University, Lutsk, Ukraine

pryvalov.yura@gmail.com

ON SOME OPTIMIZATION PROPERTIES OF THE GAUSS–WEIERSTRASS OPERATOR

Abstract. We consider the problem of the theory of function approximation concerning the analysis of linear summation methods of Fourier series, namely finding the optimal ones in one sense or another. To determine the optimal approximation order, the authors solve two important problems. First, the Gauss–Weierstrass operator is proved to be a saturated method, and its saturation order is found; second, saturation classes for this method are found.

Keywords: optimization properties of functions, Gauss–Weierstrass operator, saturation order, saturation class.

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