Sharp Remez-type inequalities for differentiable periodic functions, polynomials and splines

• Date: 2016
• Main Authors: Kofanov, V. A., Кофанов, В. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1836
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For any $\omega > 0,\; \beta \in (0, 2\omega)$, and any measurable set $B \in I_d := [0, d],\; \mu B = \beta$, we obtain the following sharp inequality of the Remez type: $$||x||_{\infty} \leq \frac{3||\varphi||_{\infty} - \varphi \biggl(\frac{\omega - \beta}2 \biggr)}{||\varphi||_{\infty...