Inequality of the Bernshtein type for polynomial splines in the space $L_2$

• Date: 1991
• Main Authors: Babenko , V. F., Pichugov , S. A., Бабенко , В. Ф., Пичугов , С. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1991
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9625
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For $2\pi$-periodic polynomial splines of order $r$, of minimal defect, with nodes at the points $k\pi /n, n\in\mathbb{N}$, there are established the sharp inequalities \[||  s^{(l)}  || _{ 2}  \leq \frac{|| \varphi _{n,r}^{(l)} || _{ 2} }{|| \Delta _h^l \varphi _{n, r} || _{ 2} }|| \Delta _h^l s||...