K. Ryutin

activity

20232025

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3 papers · 1 filter

math.FA2025

Kolmogorov widths of balls in mixed norms: the case of rigidity

Yuri Malykhin, Konstantin Ryutin

We describe the set of parameters $(p_{1}, p_{2}, q_{1}, q_{2})$ such that the balls $B_{q_{1}, q_{2}}^{s, b}$ are rigid in $ℓ_{q_{1}, q_{2}}^{s, b}$ metric i.e. they are poorly approximated by linear…

math.FA2024

Widths and rigidity of unconditional sets and random vectors

Yuri Malykhin, Konstantin Ryutin

We prove that any unconditional set in $R^{N}$ that is invariant under cyclic shifts of coordinates is rigid in $ℓ_{q}^{N}$ , $1 \leq q \leq 2$ , i.e. it can not be well approximat…

math.FA2023

Polynomial approximation on disjoint segments and amplification of approximation

Yuri Malykhin, Konstantin Ryutin

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem ha…