Best approximations and widths of classes of convolutions of periodic functions of high smoothness

被引：0
作者：
Serdyuk A.S. [1 ]
机构：
[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv
来源：
Ukrainian Mathematical Journal | 2005年 / 57卷 / 7期
关键词：
Periodic Function; Fourier Coefficient; Exponential Rate; Linear Width; High Smoothness;
D O I：
10.1007/s11253-005-0251-2
中图分类号：
学科分类号：
摘要：
We consider classes of 2π-periodic functions that are represented in terms of convolutions with fixed kernels Ψ β - whose Fourier coefficients tend to zero at exponential rate. We determine exact values of the best approximations of these classes in the uniform and integral metrics. In several cases, we determine the exact values of the Kolmogorov, Bernstein, and linear widths for these classes in the metrics of the spaces C and L. © 2005 Springer Science+Business Media, Inc.
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页码：1120 / 1148
页数：28
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