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

Keywords: isotropic Nikol'skii-Besov classes, entire function of exponential type, support of the function, Fourier transform
Published online: 2021-12-30


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 $2<p=q<\infty$, $d=1$, the established estimate is also new for the classes $S^{r}_{p,\theta}B(\mathbb{R})$.

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How to Cite
Yanchenko S., Radchenko O. Approximation Characteristics of the Isotropic Nikol’skii-Besov Functional Classes. Carpathian Math. Publ. 2021, 13 (3), 851-861.