Asymptotic Estimates for the Best Uniform Approximations of Classes of Convolution of Periodic Functions of High Smoothness

被引：0
|
作者：
Serdyuk A.S. [1 ]
Sokolenko I.V. [1 ]
机构：
[1] Institute of Mathematics of the NAS of Ukraine, Kiev
来源：
Journal of Mathematical Sciences | 2021年 / 252卷 / 4期
基金：
欧盟地平线“2020”;
关键词：
(ψβ¯) -integral; asymptotic equality; Best approximation; Fourier sum; Kolmogorov–Nikol’skii problem; Weyl–Nagy class;
D O I：
10.1007/s10958-020-05178-1
中图分类号：
学科分类号：
摘要：
We find two-sided estimates for the best uniform approximations of classes of convolutions of 2-periodic functions from a unit ball of the space Lp,1 ≤ p < ∞; with fixed kernels such that the moduli of their Fourier coefficients satisfy the condition ∑k=n+1∞ψ(k)<ψ(n): In the case of ∑k=n+1∞ψ(k)=o(1)ψ(n); the obtained estimates become the asymptotic equalities. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
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页码：526 / 540
页数：14
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