Y. Malykhin

activity

20162025

collaborators

3 papers

math.FA2025

Kolmogorov widths of the class $W_{1}^{1}$

Yuri Malykhin

We prove that $d_{n} (W_{1}^{1}, L_{q}) ≍ n^{- 1/2} lo g n$ , $2 < q < \infty$ . This completes the study of orders of decay of Kolmogorov widths for the classical case of the univariate Sobolev…

math.FA2020

Kolmogorov widths of Besov classes $B_{1, θ}^{1}$ and products of octahedra

Yuri Malykhin

In this paper we find the orders of decay for Kolmogorov widths of some Besov classes related to $W_{1}^{1}$ (the behaviour of the widths for $W_{1}^{1}$ remains unknown): $$ d_n(B^1_{1,θ}…

math.FA2016

Product of octahedra is badly approximated in the $ℓ_{2, 1}$ -metric

Yu. V. Malykhin, K. S. Ryutin

We prove that the cartesian product of octahedra $B_{1, \infty}^{n, m} = B_{1}^{n} \times \dots \times B_{1}^{n}$ ( $m$ octahedra) is badly approximated by half--dimensional subspaces in mixed--n…

Kolmogorov widths of the class W11​

Kolmogorov widths of Besov classes B1,θ1​ and products of octahedra

Product of octahedra is badly approximated in the ℓ2,1​-metric

Kolmogorov widths of the class $W_{1}^{1}$

Kolmogorov widths of Besov classes $B_{1, θ}^{1}$ and products of octahedra

Product of octahedra is badly approximated in the $ℓ_{2, 1}$ -metric