Estimates of approximation characteristics and properties of operators of the best approximation for the classes of periodic functions in the space $B_{1,1}$

• Дата: 2021
• Автори: Romanyuk, A. S., Yanchenko, S. Ya., Романюк, А. С., Янченко, С. Я.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2021
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/6755
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.51 We obtain the exact-order estimates for orthoprojection widths and similar approximation characteristics of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$ and Nikol'skii–Besov classes $B^{\boldsymbol{r}}_{p,\theta}$ of periodic functions of one and several variables in the norm of the space $B_{1,1}$. In addition, we establish that the sequence of norms of linear operators that realize the orders of the best approximation of the classes $B^{\boldsymbol{r}}_{1,\theta}$ in space $B_{1,1}$ using trigonometric polynomials with ``numbers'' of harmonics from step hyperbolic crosses is unbounded in the multidimensional case.