Approximation by Fourier sums and Kolmogorov widths for classes MBp, (Omega)(theta) of periodic functions of several variables

被引：0

作者：

Stasyuk, S. A. ^{[1
]}

机构：

[1] Ukrainian Natl Acad Sci, Inst Math, Kiev, Ukraine

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2014年 / 20卷 / 01期

关键词：

hyperbolic cross; Kolmogorov width; best approximation; mixed smoothness; Fourier sums;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain exact order estimates for approximations of mixed smoothness classes MBp,theta Omega by Fourier sums in the metric L-q for 1 < p < q < infinity. The spectrum of approximation polynomials lies in the sets generated by level surfaces of the function Omega(t)/Pi(d)(j=1) t(j)(1/p-1/q). Under some matching conditions on the parameters p, q and theta, we obtain exact order estimates for Kolmogorov widths of the classes under consideration in the metric L-q.

引用

页码：247 / 257

页数：11

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