Yurii Kolomoitsev

activity

20112024

most citedApproximation by multivariate Kantorovich-Kotelnikov operators

37 citations · 110 across the 24 of their papers we have counts for

collaborators

29 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.CA2022

On generalized $K$ -functionals in $L_{p}$ for $0 < p < 1$

Yurii Kolomoitsev, Tetiana Lomako

We show that the Peetre $K$ -functional between the space $L_{p}$ with $0 < p < 1$ and the corresponding smooth function space $W_{p}^{ψ}$ generated by the Weyl-type differential operator $ψ(…

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.NA2021

Sparse grid approximation in weighted Wiener spaces

Yurii Kolomoitsev, Tetiana Lomako, Segey Tikhonov

We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grids methods constructed with the help of quasi-interpolation operators.…

math.CA2020

Approximation by quasi-interpolation operators and Smolyak's algorithm

Yurii Kolomoitsev

We study approximation of multivariate periodic functions from Besov and Triebel--Lizorkin spaces of dominating mixed smoothness by the Smolyak algorithm constructed using a specia…

math.CA2020

Asymptotics of the Lebesgue constants for bivariate approximation processes

Yurii Kolomoitsev, Tetiana Lomako

In this paper asymptotic formulas are given for the Lebesgue constants generated by three special approximation processes related to the $ℓ_{1}$ -partial sums of Fourier series. In…

math.CA2020

Uniform approximation by multivariate quasi-projection operators

Yurii Kolomoitsev, Maria Skopina

Approximation properties of quasi-projection operators $Q_{j} (f, φ, φ)$ are studied. Such an operator is associated with a function $φ$ satisfying the Strang-Fix conditions…

math.CA2020

Approximation by multivariate quasi-projection operators and Fourier multipliers

Yurii Kolomoitsev, Maria Skopina

Multivariate quasi-projection operators $Q_{j} (f, φ, φ)$ , associated with a function $φ$ and a distribution/function $φ$ , are considered. The function $φ$ is suppo…

math.CA2020

Asymptotics of the Lebesgue constants for a $d$ -dimensional simplex

Yurii Kolomoitsev, Elijah Liflyand

In this paper an asymptotic formula is given for the Lebesgue constants generated by the anisotropically dilated $d$ -dimensional simplex. Contrary to many preceding results establi…

math.CA2020

Approximation by periodic multivariate quasi-projection operators

Yu. Kolomoitsev, A. Krivoshein, M. Skopina

Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions $φ_{j}$ and a sequence of d…

math.CA2020

Approximation properties of periodic multivariate quasi-interpolation operators

Yurii Kolomoitsev, Jürgen Prestin

We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $φ_{j}$ and trigonometric p…

math.CA2020★ 15 cited

Approximation by sampling-type operators in $L_{p}$ -spaces

Yurii Kolomoitsev, Maria Skopina

Approximation properties of the sampling-type quasi-projection operators $Q_{j} (f, φ, φ)$ for functions $f$ from anisotropic Besov spaces are studied. Error estimates in $L_…

math.CA2019★ 3 cited

Properties of moduli of smoothness in $L_{p} (R^{d})$

Yurii Kolomoitsev, Sergey Tikhonov

In this paper, we discuss various basic properties of moduli of smoothness of functions from $L_{p} (R^{d})$ , $0 < p \leq \infty$ . In particular, complete versions of Jackson-, Mar…

math.CA2019★ 3 cited

Smoothness of functions vs. smoothness of approximation processes

Yu. Kolomoitsev, S. Tikhonov

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Tw…

math.CA2018★ 37 cited

Approximation by multivariate Kantorovich-Kotelnikov operators

Yu. Kolomoitsev, M. Skopina

Approximation properties of multivariate Kantorovich-Kotelnikov type operators generated by different band-limited functions are studied. In particular, a wide class of functions w…

math.CA2018★ 4 cited

On weighted conditions for the absolute convergence of Fourier integrals

Yu. Kolomoitsev, E. Liflyand

In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are gi…

math.CA2018

Inequalities in approximation theory involving fractional smoothness in $L_{p}$ , $0 < p < 1$

Yurii Kolomoitsev, Tetiana Lomako

In the paper, we study inequalities for the best trigonometric approximations and fractional moduli of smoothness involving the Weyl and Liouville-Grünwald derivatives in $L_{p}$ , $0…

math.CA2018★ 21 cited

Quasi-projection operators in the weighted $L_{p}$ spaces

Yurii Kolomoitsev, Maria Skopina

Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorov…

math.CA2018★ 9 cited

On the growth of Lebesgue constants for convex polyhedra

Yurii Kolomoitsev, Tetiana Lomako

In the paper, new estimates of the Lebesgue constant $L (W) = \frac{1}{( 2 π ) ^{d}} \int_{T^{d}} k \in W \cap Z^{d} \sum e^{i (k, x)} d x$ …

math.CA2017

On $L_{p}$ -error of bivariate polynomial interpolation on the square

Yurii Kolomoitsev, Tetiana Lomako, Jürgen Prestin

We obtain estimates of the $L_{p}$ -error of the bivariate polynomial interpolation on the Lissajous-Chebyshev node points for wide classes of functions including non-smooth functions…

math.CA2017

Hardy-Littlewood and Ulyanov inequalities

Yurii Kolomoitsev, Sergey Tikhonov

We give the full solution of the following problem: obtain sharp inequalities between the moduli of smoothness $ω_{α} (f, t)_{q}$ and $ω_{β} (f, t)_{p}$ for $0 < p < q \leq \infty$ . A similar proble…

math.CA2017★ 13 cited

On moduli of smoothness and averaged differences of fractional order

Yurii Kolomoitsev

We consider two types of fractional integral moduli of smoothness, which are widely used in theory of functions and approximation theory. In particular, we obtain new equivalences…

math.CA2017★ 2 cited

Differential and falsified sampling expansions

Yu. Kolomoitsev, A. Krivoshein, M. Skopina

Differential and falsified sampling expansions $\sum_{k \in Z^{d}} c_{k} ϕ (M^{j} x + k)$ , where $M$ is a matrix dilation, are studied. In the case of differential expansions, $c_k=Lf(…

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

On generalized K-functionals in Lp​ for 0<p<1

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

Sparse grid approximation in weighted Wiener spaces

Approximation by quasi-interpolation operators and Smolyak's algorithm

Asymptotics of the Lebesgue constants for bivariate approximation processes

Uniform approximation by multivariate quasi-projection operators

Approximation by multivariate quasi-projection operators and Fourier multipliers

Asymptotics of the Lebesgue constants for a d-dimensional simplex

Approximation by periodic multivariate quasi-projection operators

Approximation properties of periodic multivariate quasi-interpolation operators

Approximation by sampling-type operators in Lp​-spaces

Properties of moduli of smoothness in Lp​(Rd)

Smoothness of functions vs. smoothness of approximation processes

Approximation by multivariate Kantorovich-Kotelnikov operators

On weighted conditions for the absolute convergence of Fourier integrals

Inequalities in approximation theory involving fractional smoothness in Lp​, 0<p<1

Quasi-projection operators in the weighted Lp​ spaces

On the growth of Lebesgue constants for convex polyhedra

On Lp​-error of bivariate polynomial interpolation on the square

Hardy-Littlewood and Ulyanov inequalities

On moduli of smoothness and averaged differences of fractional order

Differential and falsified sampling expansions

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

On generalized $K$ -functionals in $L_{p}$ for $0 < p < 1$

Asymptotics of the Lebesgue constants for a $d$ -dimensional simplex

Approximation by sampling-type operators in $L_{p}$ -spaces

Properties of moduli of smoothness in $L_{p} (R^{d})$

Inequalities in approximation theory involving fractional smoothness in $L_{p}$ , $0 < p < 1$

Quasi-projection operators in the weighted $L_{p}$ spaces

On $L_{p}$ -error of bivariate polynomial interpolation on the square

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