Approximation characteristics of the isotropic Nikol'skii-Besov functional classes

IF 1 Q1 MATHEMATICS

Carpathian Mathematical Publications Pub Date : 2021-12-30 DOI:10.15330/cmp.13.3.851-861

S. Yanchenko, O. Radchenko

引用次数: 0

Abstract

In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,\theta}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p,\theta}B(\mathbb{R})$. We establish the exact-order estimates for the approximation of functions from these classes $B^r_{p,\theta}(\mathbb{R}^d)$ in the metric of the Lebesgue space $L_q(\mathbb{R}^d)$, by entire functions of exponential type with some restrictions for their spectrum in the case $1 \leqslant p \leqslant q \leqslant \infty$, $(p,q)\neq \{(1,1), (\infty, \infty)\}$, $d\geq 1$. In the case $2

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各向同性Nikol'skii-Besov泛函类的逼近特性

本文研究了多变量非周期函数的各向同性Nikol'skii-Besov类$B^r_{p,\theta}(\mathbb{R}^d)$，它们对于$d = 1$等价于具有显性混合平滑的函数类$S^{r}_{p,\theta}B(\mathbb{R})$。我们在Lebesgue空间$L_q(\mathbb{R}^d)$的度规中，利用具有谱限制的指数型整体函数，在$1 \leqslant p \leqslant q \leqslant \infty$, $(p,q)\neq \{(1,1), (\infty, \infty)\}$, $d\geq 1$的情况下，建立了这些类$B^r_{p,\theta}(\mathbb{R}^d)$函数的精确阶估计。在$2

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