2019
Том 71
№ 1

All Issues

Articles: 16
Article (Ukrainian)

Estimations of the integral of modulus for mixed derivatives of the sum of double trigonometric series

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 908-921

For functions of two variables defined by trigonometric series with quasiconvex coefficients, we estimate their variations in the Hardy – Vitali sense.

Article (Ukrainian)

Approximation of analytic functions by the partial sums of Taylor series

Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1602-1619

We establish the estimates for the deviations of Taylor’s sums on the classes of analytic functions $H_\psi^\infty$, expressed via the best approximations of $\psi$-derivative functions by using the asymptotic equalities for the exact upper bounds of deviations of Taylor’s sums from functions of the same class.

Brief Communications (Ukrainian)

On the Lebesgue Inequality on Classes of $\bar{\psi}$ -Differentiable Functions

Ukr. Mat. Zh. - 2013. - 65, № 6. - pp. 844–849

We consider the deviations of Fourier sums in the spaces ${C^{\bar{\psi}}}$. The estimates of these deviations are expressed via the best approximations of the $\bar{\psi}$ -derivatives of functions in the Stepanets sense. The sequences $\bar{\psi} = (ψ_1, ψ_2)$ are quasiconvex.

Anniversaries (Ukrainian)

Oleksandr Ivanovych Stepanets’ (on the 70 th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 579-581

Article (Russian)

On necessary conditions for the convergence of Fourier series

Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 960-968

We obtain necessary conditions for the convergence of multiple Fourier series of integrable functions in the mean.

Article (Ukrainian)

On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 579–585

For the trigonometric series $$\sum_{k=0}^{\infty}a_k\sum_{l\in kV \setminus (k-1)V}e^{i(l, x)}, \quad a_k\rightarrow 0,\quad k\rightarrow \infty,$$ given on $[-\pi, \pi)^m$, where $V$ is some polyhedron in $R^m$, we prove that the inequality $$\int\limits_{T^m}\left|\sum^{\infty}_{k=0} a_k \sum_{l\in kV\setminus(k-1)V}e^{i(l, x)} \right| dx \leq C \sum^{\infty}_{k=0} (k+1) |\Delta A_k|,$$ holds if the coefficients $a_k$ satisfy the following conditions of the Sidon - Telyakovskii type: $$A_k\rightarrow\infty,\quad |\Delta a_k| \leq A_k, \quad \forall k \geq 0, \quad \sum^{\infty}_{k=0}(k+1) |\Delta A_k|<\infty.$$

Obituaries (Ukrainian)

Alexander Ivanovich Stepanets

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1722-1724

Anniversaries (Ukrainian)

Oleksandr Ivanovych Stepanets' (on his 60-th birthday)

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 579-580

Article (Russian)

On the Convergence of Fourier Series in the Space $L_1$

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 639-646

We establish necessary and sufficient conditions for the convergence in the mean of trigonometric series whose coefficients satisfy the Boas–Telyakovskii conditions.

Article (Ukrainian)

On the absolute convergence of power series

Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 594–602

We obtain a two-dimensional analog of the Hardy-Littlewood result on the absolute convergence of power series in the case of multiple series on the boundary of a unit polydisk.

Article (Ukrainian)

Estimates for the best approximation and integral modulus of continuity of a function in terms of its Fourier coefficients

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 496–503

In the integral metric, lower bounds are obtained for the best approximation and the modulus of continuity of a function in terms of its Fourier coefficients.

Article (Ukrainian)

Convergence of linear means of multiple fourier series of continuous functions

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 424-431

Article (Ukrainian)

Multidimensional analog of a result of R. Boas

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 380–383

Article (Ukrainian)

Approximation of differentiable functions of two variables in the mean by fourier sums

Ukr. Mat. Zh. - 1982. - 34, № 6. - pp. 759—765

Article (Ukrainian)

Convergence rate for Fourier partial sums on classes of continuous nonperiodic functions of two variables

Ukr. Mat. Zh. - 1980. - 32, № 1. - pp. 102 - 104

Article (Ukrainian)

Approximation of periodic functions of two variables by Vallée-Poussin sums

Ukr. Mat. Zh. - 1978. - 30, № 1. - pp. 33–44