Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables
We establish order estimates for the entropy numbers of the Nikol’skii–Besov classes $B_{p,θ}^r$ of periodic functions of many variables in the space $L_q$ with certain relations between the parameters $p$ and $q$. By using the obtained lower estimates of the entropy numbers, we establish the exact-...
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| Date: | 2015 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2015
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2088 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish order estimates for the entropy numbers of the Nikol’skii–Besov classes $B_{p,θ}^r$ of periodic functions of many variables in the space $L_q$ with certain relations between the parameters $p$ and $q$. By using the obtained lower estimates of the entropy numbers, we establish the exact-order estimates for the Kolmogorov widths of the same classes of functions in the space $L_1$. |
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