Best Approximations and Widths of Classes of Convolutions of Periodic Functions of High Smoothness
We consider classes of $2\pi$-periodic functions that are representable in terms of convolutions with fixed kernels $\Psi_{\overline{\beta}}$ whose Fourier coefficients tend to zero with the exponential rate. We compute exact values of the best approximations of these classes of functions in a uni...
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| Datum: | 2005 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3655 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We consider classes of $2\pi$-periodic functions that are representable in terms of convolutions with fixed kernels
$\Psi_{\overline{\beta}}$ whose Fourier coefficients tend to zero with the exponential rate.
We compute exact values of the best approximations of these classes of functions in a uniform and an integral metrics. In some cases, the results obtained enable
us to determine exact values of the Kolmogorov, Bernstein, and linear widths for the classes considered in the metrics of spaces $C$ and $L$. |
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