On the Jackson theorem for periodic functions in metric spaces with integral metric. II
In the spaces $L_{\psi}(T^m)$ of periodic functions with metric $\rho(f, 0)_{\psi} = \int_{T^m}\psi(|f(x)|)dx$ , where $\psi$ is a function of the type of modulus of continuity, we study the direct Jackson theorem in the case of approximation by trigonometric polynomials. It is proved that the dir...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2011
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2822 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | In the spaces $L_{\psi}(T^m)$ of periodic functions with metric $\rho(f, 0)_{\psi} = \int_{T^m}\psi(|f(x)|)dx$ , where $\psi$ is a
function of the type of modulus of continuity, we study the direct Jackson theorem in the case of approximation by trigonometric polynomials.
It is proved that the direct Jackson theorem is true if and only if the lower dilation index of the function $\psi$ is not equal to zero. |
|---|