V. Savchuk

activity

20122024

most citedApproximation of functions of several variables by linear methods in the space

S^{p}

15 citations · 21 across the 8 of their papers we have counts for

collaborators

9 papers

math.CV2024

Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean

Viktor V. Savchuk, Maryna V. Savchuk

In this paper, we study an extremal problem concerning best approximation in the Hardy space $H^{1}$ on the unit disk $D$ . Specifically, we consider weighted combinations of…

math.CA2022★ 3 cited

Approximation on hexagonal domains by Taylor-Abel-Poisson means

Jürgen Prestin, Viktor Savchuk, Andrii Shidlich

Approximative properties of the Taylor-Abel-Poisson linear summation me\-thod of Fourier series are considered for functions of several variables, periodic with respect to the hexa…

math.CV2022

Best Approximation-Preserving Operators over Hardy Space

Fahreddin. G. Abdullayev, Viktor V. Savchuk, Maryna V. Savchuk

Let $T_{n}$ be the linear Hadamard convolution operator acting over Hardy space $H^{q}$ , $1 \leq q \leq \infty$ . We call $T_{n}$ a best approximation-preserving operator (BAP operator) if $T_…

math.CV2021

Fejér-type positive operator based on Takenaka--Malmquist system on unit circle

F. G. Abdullayev, V. V. Savchuk

Let $φ = {φ_{k}}_{k = - \infty}^{\infty}$ denote the extended Takenaka--Malmquist system on unit circle $T$ and let $σ_{n, φ} (f),$ $f \in L^{1} (T)$ , be the Fejér-type operator…

math.CA2019

Approximation of functions by linear summation methods in the Orlicz type spaces

Stanislav Chaichenko, Viktor Savchuk, Andrii Shidlich

Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces $S_{M}$ . In particular, in terms of approximations by suc…

math.CA2019★ 3 cited

Approximation theorems for multivariate Taylor-Abel-Poisson means

Jürgen Prestin, Viktor Savchuk, Andrii Shidlich

We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers i…

math.CA2016

Direct and inverse approximation theorems of $2 π$ -periodic functions by Taylor--Abel--Poisson means

Jürgen Prestin, Viktor Savchuk, Andrii Shidlich

We obtain direct and inverse approximation theorems of $2 π$ -periodic functions by Taylor--Abel--Poisson operators in the integral metric.

math.CV2015

Faber Polynomials with common zero

Viktor Savchuk

We describe the two sets of meromorphic univalent functions in the class $Σ$ , for which the sequence of Faber polynomials ${F_{j}}_{j = 1}^{\infty}$ have the roots with following prop…

math.CA2012★ 15 cited

Approximation of functions of several variables by linear methods in the space $S^{p}$

Viktor V. Savchuk, Andriy L. Shidlich

In the spaces $S^{p}$ of functions of several variables, $2 π$ -periodic in each variable, we study the approximative properties of operators $A_{ϱ, r}^{△}$ and $P^\vartr…

Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean

Approximation on hexagonal domains by Taylor-Abel-Poisson means

Best Approximation-Preserving Operators over Hardy Space

Fejér-type positive operator based on Takenaka--Malmquist system on unit circle

Approximation of functions by linear summation methods in the Orlicz type spaces

Approximation theorems for multivariate Taylor-Abel-Poisson means

Direct and inverse approximation theorems of 2π-periodic functions by Taylor--Abel--Poisson means

Faber Polynomials with common zero

Approximation of functions of several variables by linear methods in the space Sp

Direct and inverse approximation theorems of $2 π$ -periodic functions by Taylor--Abel--Poisson means

Approximation of functions of several variables by linear methods in the space $S^{p}$