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arXiv · 2403.18414

Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics

M. I. Gromyak·O. Ya. Radchenko·S. Ya. Yanchenko
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Abstract

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^{\Omega}_{p,\theta}(\mathbb{R}^d)$ by sums of de la Vallee Poussin type in the metrics space $L_{\infty}(\mathbb{R}^d)$ and $L_{1}(\mathbb{R}^d)$. These classes of functions for some given $\Omega$ coincide with the well-known classical Nikol'skii-Besov isotropic classes.

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M. I. Gromyak, O. Ya. Radchenko, S. Ya. Yanchenko. 2024-03-27. Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics. https://arxiv.org/abs/2403.18414

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