Approximation of $\bar {\psi} - \text{Integrals}$ of periodic functions by Fourier sums (small smoothness). IIof periodic functions by Fourier sums (small smoothness). II
We investigate the rate of convergence of Fourier series on the classes $L^{\bar {\psi}} - \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {\psi}} - \text{N}$ are the classes of convolutions of functions from $\text{N}$ wi...
Збережено в:
| Дата: | 1998 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1998
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4938 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We investigate the rate of convergence of Fourier series on the classes $L^{\bar {\psi}} - \text{N}$ in the uniform and integral metrics. The results obtained are extended to the case where the classes $L^{\bar {\psi}} - \text{N}$ are the classes of convolutions of functions from $\text{N}$ with kernels with slowly decreasing coefficients. In particular, we obtain asymptotic equalities for the upper bounds of deviations of the Fourier sums on the sets $L^{\bar {\psi}} - \text{N}$, which are solutions of the Kolmogorov-Nikol’skii problem. In addition, we establish an analog of the well-known Lebesgue inequality. |
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