2019
Том 71
№ 7

All Issues

Golub A. P.

Articles: 23
Anniversaries (Ukrainian)

Vladyslav Kyrylovych Dzyadyk (on his 100th birthday)

Dzyadyk Yu. V., Golub A. P., Kovtunets V. V., Letychevs’kyi O. A., Lukovsky I. O., Makarov V. L., Romanyuk A. S., Samoilenko A. M., Serdyuk A. S., Shevchuk I. A., Zadiraka V. K.

Full text (.pdf)

Ukr. Mat. Zh. - 2019. - 71, № 2. - pp. 147-150

Article (Ukrainian)

Padé approximants for some classes of multivariate functions

Golub A. P., Lysenko L. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 631-640

We extend Dzyadyk’s method of generalized moment representations to the multidimensional case and, on this basis, construct and investigate the Pad´e-type approximants for some classes of multivariate functions.

Article (Ukrainian)

Existence theorems for multidimensional generalized moment representations

Golub A. P., Veselovska G.M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 4. - pp. 456-465

The conditions of existence of multidimensional generalized moment representations are established.

Article (Ukrainian)

Many-Dimensional Generalized Moment Representations and Padé -Type Approximants for Functions of Many Variables

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1166–1174

We propose an approach to the construction of multidimensional Pad´e-type approximants for analytic functions based on the extension of Dzyadyk’s method of generalized moment representations.

Article (Ukrainian)

Two-Dimensional Generalized Moment Representations and Padé Approximations for Some Humbert Series

Chernets’ka L. O., Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1315–1331

By extending Dzyadyk’s method of generalized moment representations to the case of two-dimensional number sequences, we construct and study Padé approximants for some confluent Humbert hypergeometric series.

Article (Ukrainian)

Two-Dimensional Generalized Moment Representations and Rational Approximations of Functions of Two Variables

Chernets’ka L. O., Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1035–1058

The Dzyadyk method of generalized moment representations is extended to the case of two-dimensional sequences and used to construct Padé approximants for functions of two variables.

Brief Communications (Ukrainian)

Generalized moment representations and multipoint padé approximants

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 7. - pp. 991–995

We establish conditions for the maximal dissipativity of one class of densely-defined closed linear operators in a Hilbert space. The results obtained are applied to the investigation of some special differential boundary operators.

Article (Russian)

Existence Theorems for Generalized Moment Representations

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 881-888

We establish conditions for the existence of generalized moment representations introduced by Dzyadyk in 1981.

Article (Ukrainian)

Method of Generalized Moment Representations in the Theory of Rational Approximation (A Survey)

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 3. - pp. 307-359

We give a survey of the method of generalized moment representations introduced by Dzyadyk in 1981 and its applications to Padé approximations. In particular, some properties of biorthogonal polynomials are investigated and numerous important examples are given. We also consider applications of this method to joint Padé approximations, Padé–Chebyshev approximations, Hermite–Padé approximations, and two-point Padé approximations.

Article (English)

Generalized Moment Representations and Padé Approximants Associated with Bilinear Transformations

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 623-627

By using the method of generalized moment representations with an operator of bilinear transformation of an independent variable, we construct elements of the first subdiagonal of the Padé table for certain special power series.

Article (Ukrainian)

Pade–Chebyshev Approximants for One Class of Functions

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 15-19

By using the method of generalized moment representations proposed by Dzyadyk in 1981, we construct the Pade–Chebyshev approximants for one class of functions that is an analog of the class of Markov functions.

Article (Russian)

Generalized moment representations and invariance properties of Padé approximants

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 309-314

By the method of generalized moment representations, we generalize the well-known invariance properties of Padé approximants under linear-fractional transformations of approximated functions.

Article (Ukrainian)

Generalized moment representations, biorthogonal polynomials, and Padé approximants

Golub A. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1328–1335

By using the method of generalized moment representations and certain properties of biorthogonal polynomials, we establish new invariance properties of the Padé approximants.

Article (Ukrainian)

Some properties of biorthogonal polynomials and their application to Padé approximations

Golub A. P.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 977–984

Article (Ukrainian)

On sequences that do not increase the number of real roots of polynomials

Bakan A. G., Golub A. P.

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Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1323–1331

Article (Ukrainian)

Generalized moment representations and Pade-Chebyshev approximations

Golub A. P.

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Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 762–766

Article (Ukrainian)

One type of generalized moment representations

Golub A. P.

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Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1455–1460

Article (Ukrainian)

Some properties of biorthogonal polynomials

Golub A. P.

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Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1384–1388

Article (Ukrainian)

A system of biorthogonal polynomials and its applications

Golub A. P.

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Ukr. Mat. Zh. - 1989. - 41, № 7. - pp. 961-965

Article (Ukrainian)

Generalized moment representations of basis hypergeometric series

Golub A. P.

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Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 803-808

Article (Ukrainian)

Convergence of denominators of joint pade approximations of a set of confluent hypergeometric functions

Golub A. P.

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Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 792–795

Article (Ukrainian)

Compatibility of Pade approximations of a collection of degenerate hypergeometric functions

Golub A. P.

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Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 701–706

Article (Ukrainian)

Pade approximation of arcsin z

Golub A. P.

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Ukr. Mat. Zh. - 1981. - 33, № 1. - pp. 57–60