Best mean-square approximation of functions defined on the real axis by entire functions of exponential type
Exact constants in Jackson-type inequalities are calculated in the space $L_2 (\mathbb{R})$ in the case where the quantity of the best approximation $\mathcal{A}_{\sigma}(f)$ is estimated from above by the averaged smoothness characteristic $\Phi_2(f, t) = \cfrac 1t \int^t_0||\Delta^2_h(f)||dh$. We...
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| Datum: | 2012 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2601 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Exact constants in Jackson-type inequalities are calculated in the space $L_2 (\mathbb{R})$ in the case where the quantity of the best
approximation $\mathcal{A}_{\sigma}(f)$ is estimated from above by the averaged smoothness characteristic $\Phi_2(f, t) = \cfrac 1t \int^t_0||\Delta^2_h(f)||dh$.
We also calculate the exact values of the average $\nu$-widths of classes of functions defined by $\Phi_2$. |
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