Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. I
Abstract
We prove that the kernels of analytic functions of the form Hh,β(t)=∞∑k=11coshkhcos(kt−βπ2),h>0,β∈R, satisfy Kushpel’s condition Cy,2n starting from a certain number nh explicitly expressed via the parameter h of smoothness of the kernel. As a result, for all n≥nh , we establish lower bounds for the Kolmogorov widths d2n in the space C of functional classes that can be represented in the form of convolutions of the kernel H_{h,β} with functions φ⊥1 from the unit ball in the space L_{∞}.Downloads
Published
25.06.2015
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Section
Research articles
How to Cite
Bodenchuk, V. V., and A. S. Serdyuk. “Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. I”. Ukrains’kyi Matematychnyi Zhurnal, vol. 67, no. 6, June 2015, pp. 719-38, https://umj.imath.kiev.ua/index.php/umj/article/view/2017.