Approximation characteristics of the isotropic Nikol'skii-Besov functional classes - Yanchenko, S.Ya.; Radchenko, O.Ya. (Carpathian Mathematical Publications, 2021)
In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,θ}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p,θ}B(\mathbb{R})$. We establish the exact-order estimates for the approximation of functions from these classes $B^r_{p,θ}(\mathbb{R}^d)$ 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 $1 \leqslant p \leqslant q \leqslant ∞$, $(p,q) eq \{(1,1), (∞, ∞)\}$, $d≥ 1$. In the case $2<p=q<∞$, $d=1$, the established estimate is also new for the classes $S^{r}_{p,θ}B(\mathbb{R})$.