Approximation of the periodical functions of high smoothness by the right-angled linear means of Fourier series

• Main Authors: Olga G Rovenska, Oleg Aleksandrovich Novikov
• Format: Article
• Language: Russian
• Published: Institute of Computer Science 2012-09-01
• Series: Компьютерные исследования и моделирование
• Subjects: (ψ,β)-derivative; the right-angled de la Vallee Poussin sums; Kolmogorov–Nikol'skiy problem
• Online Access: http://crm.ics.org.ru/uploads/crmissues/crm_2012_3/521-529.pdf
• ISSN: 2076-7633; 2077-6853

We obtain asymptotic equalities for upper bounds of the deviations of the right-angled de la Vallee Poussin sums taken over classes of periodical functions of many variables of high smoothness. These equalities guarantee the solvability of the Kolmogorov-Nikolskii problem for the right-angled de la Vallee Poussin sums on the specified classes of functions.