2019
Том 71
№ 11

Kharkevych Yu. I.

Articles: 22
Article (Ukrainian)

Isometry of the subspaces of solutions of systems of differential equations to the spaces of real functions

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1011-1027

UDC 517.5
We determine the subspaces of solutions of the systems of Laplace and heat-conduction differential equations isometric to the corresponding spaces of real functions determined on the set of real numbers.

Brief Communications (Ukrainian)

On the asymptotic of associate sigma-functions and Jacobi theta-functions

Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1149-1152

For the associated sigma-functions, Jacobi theta-functions, and their logarithmic derivatives, we present asymptotic formulas valid outside an efficiently constructed exceptional sets of discs.

Article (Ukrainian)

Approximating properties of biharmonic Poisson operators in the classes $\hat{L}^{\psi}_{\beta, 1}$

Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 650-656

We obtain the asymptotic equalities for the least upper bounds of the approximations of functions from the classes $\hat{L}^{\psi}_{\beta, 1}$ by biharmonic Poisson operators in the integral metric.

Article (Ukrainian)

I. Approximative properties of biharmonic Poisson integrals in the classes $W^r_{\beta} H^{\alpha}$

Ukr. Mat. Zh. - 2016. - 68, № 11. - pp. 1493-1504

We deduce asymptotic equalities for the least upper bounds of approximations of functions from the classes $W^r_{\beta} H^{\alpha}$, and $H^{\alpha}$ by biharmonic Poisson integrals in the uniform metric.

Brief Communications (Russian)

On the Asymptotics of Some Weierstrass Functions

Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 135–138

For Weierstrass functions σ(z) and ζ(z), we present the asymptotic formulas valid outside the efficiently constructed exceptional sets of discs that are much narrower than in the known asymptotic formulas.

Article (Ukrainian)

Approximation of (ψ, β)-differentiable functions of low smoothness by biharmonic Poisson integrals

Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1602-1622

We solve the Kolmogorov – Nikol’skii problem for biharmonic Poisson integrals on the classes of (ψ, β)- differentiable periodic functions of low smoothness in the uniform metric.

Article (Ukrainian)

Approximation of functions from the classes $C^{\psi}_{\beta, \infty}$ by biharmonic Poisson integrals

Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 939-959

Asymptotic equalities are obtained for upper bounds of deviations of biharmonic Poisson integrals on the classes of $(\psi, \beta)$-differentiable periodic functions in the uniform metric.

Brief Communications (Ukrainian)

Nevanlinna characteristics and defective values of the Weierstrass zeta function

Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 718-720

We establish the Nevanlinna characteristics of the Weierstrass zeta function and show that none of the values $a \in \overline{C}$ is exceptional in the Nevanlinna sense for this function.

Article (Ukrainian)

Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric

Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1497-1515

We obtain asymptotic equalities for upper bounds of approximations of functions from the class $C_{β,∞} ψ$ by Poisson integrals in the metric of the space $C$.

Article (Ukrainian)

Approximation of conjugate differentiable functions by biharmonic Poisson integrals

Ukr. Mat. Zh. - 2009. - 61, № 3. - pp. 333-345

We determine the exact values of upper bounds of approximations by biharmonic Poisson integrals on classes of conjugate differentiable functions in uniform and integral metrics.

Article (Ukrainian)

Approximation of conjugate differentiable functions by their Abel–Poisson integrals

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 73-82

We obtain the exact values of upper bounds of approximations of classes of periodic conjugate differentiable functions by their Abel–Poisson integrals in uniform and integral metrics.

Article (Ukrainian)

Approximation of functions from the class $\hat{C}^{\psi}_{\beta, \infty}$ by Poisson biharmonic operators in the uniform metric

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 669 – 693

We obtain asymptotic equalities for upper bounds of approximations of functions from the class $\hat{C}^{\psi}_{\beta, \infty}$ by the Poisson biharmonic operators in the uniform metric.

Article (Russian)

Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals

Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1105–1115

Complete asymptotic decompositions are obtained for values of exact upper bounds of approximations of functions from the classes $W^r_1,\quad r \in N,$ and WJr, $\overline{W}^r_1,\quad r \in N\backslash\{1\}$, by their biharmonic Poisson integrals.

Article (Ukrainian)

Approximation of (ψ, β)-differentiable functions by Weierstrass integrals

Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 953–978

Asymptotic equalities are obtained for upper bounds of approximations of functions from the classes $C^{\psi}_{\beta \infty}$ and $L^{\psi}_{\beta 1}$ by the Weierstrass integrals.

Article (Ukrainian)

Approximation of classes of periodic multivariable functions by linear positive operators

Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 12–19

In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation does not exceed the sum of properly chosen least upper bounds in m-and ((N ? m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality.

Article (Ukrainian)

Approximation of $(\psi, \beta)$-Differentiable Functions Defined on the Real Axis by Abel-Poisson Operators

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1097 – 1111

We obtain asymptotic equalities for upper bounds of approximations of functions on the classes $\hat C_{\beta ,\infty }^\psi$ and $\hat L_{\beta ,1}^\psi$ by Abel-Poisson operators.

Article (Ukrainian)

Approximation of functions defined on the real axis by operators generated by λ-methods of summation of their Fourier integrals

Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1267-1280

We obtain asymptotic equalities for upper bounds of the deviations of operators generated by λ-methods (defined by a collection Λ={λσ(·)} of functions continuous on [0; ∞) and depending on a real parameter σ) on classes of (ψ, β)-differentiable functions defined on the real axis.

Article (Ukrainian)

Approximation of Differentiable Periodic Functions by Their Biharmonic Poisson Integrals

Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1213-1219

We determine the exact values and asymptotic decompositions of upper bounds of approximations by biharmonic Poisson integrals on classes of periodic differentiable functions.

Article (Ukrainian)

Complete Asymptotics of the Deviation of a Class of Differentiable Functions from the Set of Their Harmonic Poisson Integrals

Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 43-52

On a class of differentiable functions W r and the class $\overline W ^r$ of functions conjugate to them, we obtain a complete asymptotic expansion of the upper bounds $\mathcal{E}(\mathfrak{N},A\rho )_C$ of deviations of the harmonic Poisson integrals of the functions considered.

Brief Communications (Ukrainian)

On the Approximation of Functions of the Hölder Class by Triharmonic Poisson Integrals

Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 855-859

We determine the exact value of the upper bound for the deviation of the triharmonic Poisson integral from functions of the Hölder class.

Brief Communications (Ukrainian)

On the Approximation of Functions of the Hölder Class by Biharmonic Poisson Integrals

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 971-974

We determine the exact value of the upper bound of the deviation of biharmonic Poisson integrals from functions of the Hölder class.