Bernstein-type inequalities for splines defined on the real axis

• Date: 2011
• Main Authors: Babenko, V. F., Zontov, V. A., Бабенко, В. Ф., Зонтов, В. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2746
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain the exact inequalities of the Bernstein type for splines $s \in S_{m, h} \bigcap L_2 (\mathbb{R})$ as well as the exact inequalities that, for splines $s \in S_{m, h}, \quad h > 0$, estimate $L_p$-norms of the Fourier transforms of their $k$-th derivative by $L_p$-norms of the Four...