Yurii Kolomoitsev

collaborators

4 papers

math.CA2024

Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

Yurii Kolomoitsev, Sergey Tikhonov

We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results…

math.NA2022

Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models

Gerlind Plonka, Yannick Riebe, Yurii Kolomoitsev

We analyze the structure of a one-dimensional deep ReLU neural network (ReLU DNN) in comparison to the model of continuous piecewise linear (CPL) spline functions with arbitrary kn…

math.CA2022

Sharp $L_{p}$ -error estimates for sampling operators

Yurii Kolomoitsev, Tetiana Lomako

We study approximation properties of linear sampling operators in the spaces $L_{p}$ for $1 \leq p < \infty$ . By means of the Steklov averages, we introduce a new measure of smoothness t…

math.CA2016

Best approximations and moduli of smoothness of functions and their derivatives in $L_{p}$ , $0 < p < 1$

Yurii Kolomoitsev

Several new inequalities for moduli of smoothness and errors of the best approximation of a function and its derivatives in the spaces $L_{p}$ , $0 < p < 1$ , are obtained. For example, it…

Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models

Sharp Lp​-error estimates for sampling operators

Best approximations and moduli of smoothness of functions and their derivatives in Lp​, 0<p<1

Sharp $L_{p}$ -error estimates for sampling operators

Best approximations and moduli of smoothness of functions and their derivatives in $L_{p}$ , $0 < p < 1$