Entropy numbers and the widths of the classes $B_{p,θ}^r$ of periodic functionsof many variables

• Дата: 2016
• Автори: Romanyuk, A. S., Романюк, А. С.
• Формат: Стаття
• Мова: Російська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2016
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/1928
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We establish the exact order estimates for the entropy numbers of the Nikol’skii – Besov classes of periodic functions of two variables in the space $L_\infty$ and use the obtained results in estimating the lower bounds for Kolmogorov, linear, and trigonometric widths. We also study the behavior of...