Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. I

• Date: 2015
• Main Authors: Bodenchuk, V. V., Serdyuk, A. S., Боденчук, В. В., Сердюк, А. С.
• 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/2017
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that the kernels of analytic functions of the form $${H}_{h,\beta }(t)={\displaystyle \sum_{k=1}^{\infty}\frac{1}{ \cosh kh} \cos \left(kt-\frac{\beta \pi }{2}\right),}h>0,\beta \in \mathbb{R},$$ satisfy Kushpel’s condition $C_{y,2n}$ starting from a certain number $n_h$ explicitly e...