2019
Том 71
№ 11

# Holub A. P.

Articles: 24
Article (Ukrainian)

### Generalized moment representations and multivariate multipoint Padé-type approximants

Ukr. Mat. Zh. - 2019. - 71, № 10. - pp. 1331-1346

UDC 517.53
Dzyadyk's method of generalized moment representations is used to construct and study bivariate two-point Pad\'e-type approximants.

Anniversaries (Ukrainian)

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

Article (Ukrainian)

### Padé approximants for some classes of multivariate functions

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

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

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

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

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

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

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)

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

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

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

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 (Russian)

### Generalized moment representations, biorthogonal polynomials, and Padé approximants

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 (Russian)

### Some properties of biorthogonal polynomials and their application to Padé approximations

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

Transformations of biorthogonal polynomials under certain transformations of biorthogonalizable sequences are studied. The obtained result is used to construct Padé approximants of orders $[N−1/N],\; N \in ℕ,$ for the functions $$\tilde f(z) = \sum\limits_{m = 0}^M {\alpha _m } \frac{{f(z) - T_{m - 1} [f;z]}}{{z^m }},$$ where $f(z)$ is a function with known Padé approximants of the indicated orders, $T_j [f;z]$ are Taylor polynomials of degreej for the function $f(z)$, and $α_{ m, M} = \overline {1,M}$ are constants.

Article (Russian)

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

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

A complete description is given for the sequences $\{λ_k}_{k = 0}^{ ∞}$ such that, for an arbitrary real polynomial $f(t) = \sum\nolimits_{k = 0}^n {a_k t^k }$, an arbitrary $A \in (0, +∞)$, and a fixed $C \in (0,+∞)$, the number of roots of the polynomial $(Tf)(t) = \sum\nolimits_{k = 0}^n {a_k \lambda _k t^k }$ on $[0,C]$ does not exceed the number of roots off $(t)$ on $[0, A]$.

Article (Ukrainian)

### Generalized moment representations and Pade-Chebyshev approximations

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

Article (Ukrainian)

### One type of generalized moment representations

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

Article (Ukrainian)

### Some properties of biorthogonal polynomials

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

Article (Ukrainian)

### A system of biorthogonal polynomials and its applications

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

Article (Ukrainian)

### Generalized moment representations of basis hypergeometric series

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

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

Article (Ukrainian)

### Compatibility of Pade approximations of a collection of degenerate hypergeometric functions

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

Article (Ukrainian)

### Pade approximation of arcsin z

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