Inequalities for Nonperiodic Splines on the Real Axis and Their Derivatives

• Date: 2014
• Main Authors: Kofanov, V. A., Кофанов, В. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2125
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We solve the following extremal problems: (i) \( {\left\Vert {s}^{(k)}\right\Vert}_{L_q\left[\alpha, \beta \right]}\to \sup \) and (ii) \( {\left\Vert {s}^{(k)}\right\Vert}_{W_q}\to \sup \) over all shifts of splines of order r with minimal defect and nodes at the points lh, l ∈ Z , such that L(...