On the estimates of widths of the classes of functions defined by the generalized moduli of continuity and majorants in the weighted space $L_{2x} (0,1)$
The upper and lower estimates for the Kolmogorov, linear, Bernstein, Gelfand, projective, and Fourier widths are obtained in the space $L_{2,x}(0, 1)$ for the classes of functions $W^r_2 (\Omega^{(\nu )}_{m,x}; \Psi )$, where $r \in Z+, m \in N, \nu \geq 0,$ and $\\Omega^{(\nu )}_{m,x}$ and $\Ps...
Збережено в:
| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2019
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1430 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | The upper and lower estimates for the Kolmogorov, linear, Bernstein, Gelfand, projective, and Fourier widths are obtained
in the space $L_{2,x}(0, 1)$ for the classes of functions $W^r_2 (\Omega^{(\nu )}_{m,x}; \Psi )$, where $r \in Z+, m \in N, \nu \geq 0,$ and $\\Omega^{(\nu )}_{m,x}$ and $\Psi$
are the mth order generalized modulus of continuity and the majorant, respectively. The upper and lower estimates for
the suprema of Fourier – Bessel coefficients were also found on these classes. We also present the conditions for majorants
under which it is possible to find the exact values of indicated widths and the suprema of Fourier – Bessel coefficients. |
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