On the best $L_1$-approximations of functional classes by splines under restrictions imposed on their derivatives

• Date: 1999
• Main Authors: Babenko, V. F., Parfinovych, N. V., Бабенко, В. Ф., Парфинович, Н. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4629
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We find the exact asymptotics ($n → ∞$) of the best $L_1$-approximations of classes $W_1^r$ of periodic functions by splines $s ∈ S_{2n, r∼-1}$ ($S_{2n, r∼-1}$ is a set of $2π$-periodic polynomial splines of order $r−1$, defect one, and with nodes at the points $kπ/n,\; k ∈ ℤ$) such that $V_0^{2π} s...