Order Estimates for the Best Orthogonal Trigonometric Approximations of the Classes of Convolutions of Periodic Functions of Low Smoothness

• Date: 2015
• Main Authors: Serdyuk, A. S., Stepanyuk, T. A., Сердюк, А. С., Степанюк, Т. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2033
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish order estimates for the best uniform orthogonal trigonometric approximations on the classes of $2π$-periodic functions whose $(ψ, β)$-derivatives belong to unit balls in the spaces $L_p,\; 1 ≤ p < ∞$, in the case where the sequence $ψ(k)$ is such that the product $ψ(n)n^{1/p}$ ma...