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...
Gespeichert in:
| Datum: | 2011 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2011
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2822 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
|---|