Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes
We obtain exact Jackson-type inequalities in the case of the best mean square approximation by entire functions of finite degree $≤ σ$ on a straight line. For classes of functions defined via majorants of averaged smoothness characteristics $Ω_1(f, t ),\; t > 0$, we determine the exact values...
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| Дата: | 2010 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2010
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2935 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We obtain exact Jackson-type inequalities in the case of the best mean square approximation by entire functions of finite degree $≤ σ$ on a straight line. For classes of functions defined via majorants of averaged smoothness characteristics $Ω_1(f, t ),\; t > 0$, we determine the exact values of the Kolmogorov mean ν-width, linear mean ν-width, and Bernstein mean $ν$-width, $ν > 0$. |
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