Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics
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| Format: | Preprint |
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2024
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| _version_ | 1866916180019642368 |
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| author | Gromyak, M. I. Radchenko, O. Ya. Yanchenko, S. Ya. |
| author_facet | Gromyak, M. I. Radchenko, O. Ya. Yanchenko, S. Ya. |
| contents | We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^Ω_{p,θ}(\mathbb{R}^d)$ 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 $Ω$ coincide with the well-known classical Nikol'skii-Besov isotropic classes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_18414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics Gromyak, M. I. Radchenko, O. Ya. Yanchenko, S. Ya. Classical Analysis and ODEs 41A30, 41A50, 41A63, 42A38 We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes $B^Ω_{p,θ}(\mathbb{R}^d)$ 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 $Ω$ coincide with the well-known classical Nikol'skii-Besov isotropic classes. |
| title | Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics |
| topic | Classical Analysis and ODEs 41A30, 41A50, 41A63, 42A38 |
| url | https://arxiv.org/abs/2403.18414 |