On exact Bernstein-type inequalities for splines

• Datum: 2006
• Hauptverfasser: Kofanov, V. A., Кофанов, В. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2006
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3538
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We establish new exact Bernstein-type and Kolmogorov-type inequalities. The main result of this work is the following exact inequality for periodic splines $s$ of order $r$ and defect 1 with nodes at the points $iπ/n, i ∈ Z, n ∈ N:$ $$\left\| {s^{(k)} } \right\|_q \leqslant n^{k + 1/p - 1/q} \frac{...