Approximation of some classes of functions of many variables by harmonic splines

• Date: 2012
• Main Authors: Babenko, V. F., Leskevich, T. Yu., Бабенко, В. Ф., Лескевич, Т. Ю.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2636
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We determine the exact values of upper bounds of the error of approximation by harmonic splines for functions $u$ defined on an $n$-dimensional parallelepiped $\Omega$ forwhich $||\Delta u||_{L_{\infty}(\Omega)} \leq 1$ and for functions $u$ defined on $\Omega$ forwhich $||\Delta u||_{L_{p}(\Omega)}...