Approximation of $\overline \psi$-Integrals of Periodic Functions by de la Vallée-Poussin Sums (Low Smoothness)

• Date: 2001
• Main Authors: Rukasov, V. I., Chaichenko, S. O., Рукасов, В. И., Чайченко, С. О.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4384
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the asymptotic behavior of the upper bounds of deviations of linear means of Fourier series from the classes $C_{\infty} ^{\psi}$. In particular, we obtain asymptotic equalities that give a solution of the Kolmogorov – Nikol'skii problem for the de la Vallée-Poussin sums on...