2018
Том 70
№ 8

All Issues

Dzyadyk V. K.

Articles: 31
Brief Communications (Ukrainian)

Remark on the Lebesgue constant in the Rogosinski Kernel

Dzyadyk V. K., Shevchuk I. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 1002–1004

For every n, we compute the Lebesgue constant of Rogosinski kernel with any preassigned accuracy.

Brief Communications (Ukrainian)

To the memory of Valentin Anatol'evich Zmorovich

Baranovskii F. T., Berezansky Yu. M., Buldygin V. V., Daletskii Yu. L., Dobrovol'skii V. A., Dzyadyk V. K., Lozovik V. G., Mitropolskiy Yu. A., Samoilenko A. M., Skrypnik I. V., Tamrazov P. M., Yaremchuk F. P.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1110–1111

Article (Ukrainian)

Convergence of an algorithm for constructing snakes

Dzyadyk V. K., Kovtunets V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 7. - pp. 825–832

Article (Ukrainian)

Approximation method of solution of boundary problems

Dzyadyk V. K., Ostrovetskii L. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 378–379

Article (Ukrainian)

Evgeny Yakovlevich Remez (on his ninetieth birthday)

Dzyadyk V. K., Gavrilyuk V. T., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 128–131

Article (Ukrainian)

The A-method and rational approximation

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 2. - pp. 250–252

Article (Ukrainian)

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 567 – 571

Article (Ukrainian)

Generalized problem of moments and the pade approximation

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 297 — 302

Article (Ukrainian)

Asymptotic behavior of Lebesgue constants in trigonometric interpolation

Dzyadyk S. Yu., Dzyadyk V. K., Prypik A. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1981. - 33, № 6. - pp. 736-744

Article (Ukrainian)

Estimation of error of polynomial approximation of solutions of ordinary differential equations

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 1. - pp. 83–89

Article (Ukrainian)

Approximation to functions of a complex variable on arcs

Dzyadyk V. K.

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Ukr. Mat. Zh. - 1977. - 29, № 2. - pp. 254–259

Article (Ukrainian)

On A. N. Kolmogorov's inequalities relating the upper bounds of derivatives of real functions defined on the whole axis

Dubovik V. A., Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1975. - 27, № 3. - pp. 291–299

Article (Ukrainian)

A contribution to kolmogorov problem of relationships among upper bounds of derivatives of real functions given on entire axis

Dubovik V. A., Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 3. - pp. 300–317

Article (Ukrainian)

On the efficient construction of polynomials which realize near-to-best approximation of the functions ex, sin x, etc.

Dzyadyk V. K.

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Ukr. Mat. Zh. - 1973. - 25, № 4. - pp. 435—453

Article (Ukrainian)

Method of expanding unity in regions with piecewise smooth boundaries as sums of algebraic polynomials of two variables having certain properties of a kernel

Dzyadyk V. K., Konovalov V. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 2. - pp. 179—192

Article (Ukrainian)

On limiting values of an integral of Cauchy type for functions of zygmund classes

Dzyadyk V. K., Shevchuk I. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 5. - pp. 601–617

Article (Ukrainian)

Asymptotic equations for the supremums of approximations of functions of hölder's classes by rogosinski polynomials

Dzyadyk V. K., Stepanets O. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 4. - pp. 476–487

Article (Ukrainian)

On the application of generalized Faber polynomials to the approximation of Cauchy-type integrals and functions of classes Ar in domains with a smooth and a piecewise-smooth boundary

Dzyadyk V. K.

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Ukr. Mat. Zh. - 1972. - 24, № 1. - pp. 3–19

Article (Ukrainian)

One method of constructing Tikhonov-type normals in the solution of systems of linear equations

Dzyadyk V. K.

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Ukr. Mat. Zh. - 1971. - 23, № 2. - pp. 235–239

Article (Ukrainian)

On the application of linear methods to the approximation by polynomials of functions which are solutions of Fredholm integral equations of the second kind II

Dzyadyk V. K.

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Ukr. Mat. Zh. - 1970. - 22, № 5. - pp. 579—590

Article (Ukrainian)

On the application of linear methods to the approximation by polynomials of functions which are solutions of Fredholm integral equations of the second kind. I

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1970. - 22, № 4. - pp. 461–480

Article (Ukrainian)

Exact upper bound for approximations on classes of differential periodic functions using Rogosinski polynomials

Dzyadyk V. K., Gavrilyuk V. T., Stepanets O. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1970. - 22, № 4. - pp. 481–493

Article (Russian)

Investigations in the theory of the approximation of analytic functions carried out at the Mathematics Institute, Academy of Sciences of the Ukrainian SSR

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1969. - 21, № 2. - pp. 173–192

Article (Ukrainian)

On a constructive characteristic of functions of Hölder classes on closed sets with a piece-wise smooth boundary admitting zero angles

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1968. - 20, № 5. - pp. 603–619

Article (Ukrainian)

Estimate of residue for some cubature formulas

Dzyadyk V. K., Panasovich V. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1968. - 20, № 2. - pp. 147–155

Article (Ukrainian)

Analytic and harmonic transformations and the approximation of harmonic functions

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 5. - pp. 33–57

Brief Communications (Russian)

A simple example of a continuous periodic function Unexpandable into a Fourier series

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 4. - pp. 103-104

Article (Russian)

On the approximation of analytical functions in regions with a smooth boundary

Dzyadyk V. K., Galan D. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 1. - pp. 26-38

Article (Russian)

Converse theorems of the theory of approximation of functions in complex regions

Dzyadyk V. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 4. - pp. 365-375

An inequality is established for the modulus of the derivative of the algebraic polynomial $P_n(z)$ of degree $n$ to the effect that if, on an analytic arc $C$ on a piecewise-smooth boundary $C$ of a simply connected region $G$, $P_n(z)$ satisfies the condition $$|P_n(z)| \leq [\varrho_{l+1/n} (z)]^s \omega|\varrho_{l+1/n}(z)|, \quad(1)$$ where $\omega(t)$ is some modulus of continuity, $\varrho_{l+1/n}(z)$ is the distance from $z \in C$ to the $n$th line of level $C_n$ (i.e. to the line $\Phi(z) = R\left(1 + \cfrac1n\right)$, where $\Phi(z)$ is the mapping function of the outside $C$ on the outside of a unit circle, and $R$ is the conforming radius, $G$ and $s \leq 0$ then $$|P^1_n(z)| \leq A[\varrho_{l+1/n}(z)]^{s-1}\omega [\varrho_{l+1/n}(z)], A = const \quad(2)$$ After thjs an estimate is given of the continuity modulus of the rth derivative ($z$ is a whole number $\leq 0$) of the function $f(z)$ on $C$ under the condition that with each natural $n$ a polynomial $P,(z)$ can be found for it, such that $$|f(z) — P^1-n(z)| \leq [\varrho_{l+1/n}(z)]^r\omega [\varrho_{l+1/n}(z)]\quad(3)$$

Brief Communications (Russian)

Approximation of nonperiodic functions of polynomials on a system of segments

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 1. - pp. 88-94

Brief Communications (Russian)

On a property of almost periodic polynomials

Dzyadyk V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 96-98