Best “Continuous” $n$-Term Approximations in the Spaces $S_\phi ^p$

• Date: 2003
• Main Authors: Rukasov, V. I., Stepanets, O. I., Рукасов, В. И., Степанец, А. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2003
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3941
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We find exact values of upper bounds for the best approximations of $q$-ellipsoids by polynomials of degree $n$ in the spaces $S_\phi ^p$ in the case where the approximating polynomials are constructed on the basis of $n$-dimensional subsystems chosen successively from a given orthonormal system ϕ.