# Dovgoshei A. A.

### On the Statistical Convergence of Metric-Valued Sequences

Değer U., Dovgoshei A. A., Küçükaslan M.

Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 712–720

We study the conditions for the density of a subsequence of a statistically convergent sequence under which this subsequence is also statistically convergent. Some sufficient conditions of this type and almost converse necessary conditions are obtained in the setting of general metric spaces.

### Betweenness relation and isometric imbeddings of metric spaces

Dordovskii D. V., Dovgoshei A. A.

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1319-1328

We give an elementary proof of the classical Menger result according to which any metric space *X* that consists of more than four points is isometrically imbedded into \( \mathbb{R} \) if every three-point subspace of *X* is isometrically imbedded into \( \mathbb{R} \). A series of corollaries of this theorem is obtained. We establish new criteria for finite metric spaces to be isometrically imbedded into \( \mathbb{R} \).

### Analyticity of Higher-Order Moduli of Continuity of Real-Analytic Functions

Dovgoshei A. A., Potemkina L. L.

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 750-761

The Perel'man's result according to which the first modulus of continuity of any real-analytic function *f* is a function analytic in a certain neighborhood of the origin is generalized to the case of arbitrary moduli of continuity of higher order.

### Three-Term Recurrence Relation for Polynomials Orthogonal with Respect to Harmonic Measure

Ukr. Mat. Zh. - 2001. - 53, № 2. - pp. 147-155

We prove that a three-term recurrence relation for analytic polynomials orthogonal with respect to harmonic measure in a simply connected domain *G* exists if and only if ∂*G* is an ellipse.

### Chebyshev polynomial approximation on a closed subset with unique limit point and analytic extension of functions

Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 891-900

We describe the domain of analyticity of a continuous function *f* in terms of the sequence of the best polynomial approximations of *f* on a compact set *K*(*K* ⊂ ℂ) and the sequence of norms of Chebyshev polynomials for *K*.

### Some properties of polynomials orthogonal in a space with “intermediate” topology. Kernel function and extremal properties

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 915–923

A space of holomorphic functions is considered. A topology in this space is “intermediate” between the topology of uniform convergence and the topology of uniform convergence on compact sets. The properties of systems of orthonormal polynomials are studied in Hilbert spaces with this topology.

### Families of functions with equiabsolutely continuous integrals

Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 178–184

The approximation of functions from Hardy classes by bounded analytic functions is investigated. A theorem is proved, characterizing the sets of functions with equiabsolutely continuous integrals as limit points of the family of bounded subsets of the space H^{∞}.