Апроксимаційні характеристики класів типу Нікольського-Бєсова періодичних функцій багатьох змінних у просторі $B_{q,1}$

IF 1 Q1 MATHEMATICS
O. V. Fedunyk-Yaremchuk, S. B. Hembars’ka, I.A. Romanyuk, P. V. Zaderei
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引用次数: 0

Abstract

We obtained the exact order estimates of approximation of periodic functions of several variables from the Nikol'skii-Besov-type classes $B^{\Omega}_{p,\theta}$ by using their step hyperbolic Fourier sums in the space $B_{q,1}$. The norm in this space is stronger than the $L_q$-norm. In the considered situations, approximations by the mentioned Fourier sums realize the orders of the best approximations by polynomials with "numbers" of harmonics from the step hyperbolic cross. We also established the exact order estimates of the Kolmogorov, linear and trigonometric widths of classes $B^{\Omega}_{p,\theta}$ in the space $B_{q,1}$ for certain relations between the parameters $p$ and $q$.
空间 $B_{q,1}$ 中多变量周期函数的尼克尔斯基-贝索夫类型类的近似特征
我们通过在空间 $B_{q,1}$ 中使用它们的阶跃双曲傅里叶和,从尼克尔斯基-贝索夫类型类 $B^{\Omega}_{p,\theta}$ 中获得了几个变量的周期函数近似的精确阶次估计。该空间中的规范比 $L_q$ 规范更强。在所考虑的情况下,用上述傅里叶和进行的近似实现了用阶跃双曲交叉谐波 "数 "的多项式进行的最佳近似的阶数。对于参数 $p$ 和 $q$之间的某些关系,我们还建立了在空间 $B_{q,1}$ 中类 $B^{Omega}_{p,\theta}$ 的柯尔莫哥洛夫、线性和三角宽度的精确阶数估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
25 weeks
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