Generalized characteristics of smoothness and some extremе problems of the approximation theory of functions in the space $L_2 (R)$. I

• Date: 2018
• Main Authors: Vakarchuk, S. B., Вакарчук, С. Б.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1627
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the generalized characteristics of smoothness of the functions $\omega^w(f, t)$ and $\Lambda^w(f, t), t > 0,$ in the space $L_2(R)$ and, on the classes $L^{\alpha}_2 (R)$ defined with the help of fractional-order derivatives $\alpha \in (0,\infty)$, obtain the exact Jackson-ty...