Yuri Malykhin

activity

20242026

collaborators

4 papers

math.FA2026

Low-dimensional approximation of uniformly bounded orthonormal systems

Yuri Malykhin

We prove that if $f_{1}, \dots, f_{N}$ is an uniformly bounded orthonormal system, then for all $p \in [1, 2)$ there is an estimate for its Kolmogorov widths: $d_n(\{f_1,\dots,f_N\},L_p) \…

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

On the structure of low-rank matrices that approximate the identity matrix

Yuri Malykhin

Consider a matrix $A$ of rank $n$ that approximates the $N \times N$ identity matrix with elementwise error at most $1/3$ . We give a lower bound on the number of elements s.t. $|A_{…

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…