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<p>We consider the problem of the function approximation theory concerning the analysis of linear methods of Fourier series summation, namely, finding the optimal ones in one sense or another. To determine the optimal approximation order, we solve two important problems. First, we prove that the Gauss–Weierstrass operator is a saturated method, and we find its saturation order; second, we find saturation classes for this method.</p>

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On Some Optimization Properties of the Gauss–Weierstrass Operator

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • I. V. Kal’chuk,
  • Y. V. Pryvalov

摘要

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