On Piecewise-Constant Approximation of Continuous Functions of n Variables in Integral Metrics

• Date: 2002
• Main Authors: Bel'skii, S. A., Бельский, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4066
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form ω(δ1, ..., δ n ) = ω1(δ1) + ... + ω n (δ n ), where ω i (δ i ) are ordinary moduli of continuity that depend on one variable. In the case where ω i (δ...