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

  • V. V. Bodenchuk
  • A. S. Serdyuk

Abstract

We prove that the kernels of analytic functions of the form Hh,β(t)=k=11coshkhcos(ktβπ2),h>0,βR, 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 nnh , 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 Hh,β with functions φ1 from the unit ball in the space L.
Published
25.06.2015
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.
Section
Research articles