Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions

IF 1 Q1 MATHEMATICS

Carpathian Mathematical Publications Pub Date : 2023-06-14 DOI:10.15330/cmp.15.1.78-94

A. Romanyuk, V. Romanyuk, K. Pozharska, S. Hembars’ka

引用次数: 2

Abstract

Exact order estimates for some characteristics of linear and nonlinear approximation of the isotropic Nikol'skii-Besov classes $\mathbf{B}^r_{p,\theta}$ of periodic multivariate functions in the spaces $B_{q,1}$, $1\leq q \leq \infty$, are obtained. Among them are the best orthogonal trigonometric approximations, best $m$-term trigonometric approximations, Kolmogorov, linear and trigonometric widths. For all considered characteristics, their estimates coincide in order with the corresponding estimates in the spaces $L_{q}$. Moreover, the obtained exact in order estimates (except the case $1

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周期多元函数各向同性类的线性和非线性逼近的特征

得到了周期多元函数的各向同性Nikol'skii-Besov类$\mathbf{B}^r_{p,\theta}$在$B_{q,1}$, $1\leq q \leq \infty$空间中线性和非线性近似的某些特征的精确阶估计。其中有最佳正交三角近似、最佳$m$ -项三角近似、Kolmogorov、线性宽度和三角宽度。对于所有考虑的特征，它们的估计与$L_{q}$中相应的估计顺序一致。此外，所获得的精确的有序估计(除了$1

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