2019
Том 71
№ 11

# Krutigolova Ye. K.

Articles: 7
Article (Ukrainian)

### Representation of analytic functions by generalized series of exponents in unbounded convex domains

Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 812–817

We establish conditions for the representation of functions f(z) analytic in unbounded convex domains D and continuous in $\bar D$ via series of the form $\sum\nolimits_{n = 1}^\infty {P_n \left( z \right)} e^{\lambda _n z}$ .

Brief Communications (Russian)

### On conditions for convergence of Taylor-Dirichlet series in a convex domain

Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1576-1581

We establish necessary and sufficient conditions for the absolute convergence of the series $$\mathop \sum \limits_{v = 1}^\infty \sum\limits_{k = 0}^{m_v - I} {a_{v,k} z^k \exp (\lambda _v z)}$$ in an open region. We also give conditions under which an arbitrary function analytic in a closed region (analytic in an open region and continuous in a closed region) can be represented by a series of this type.

Article (Ukrainian)

### Properties of exponential series, the exponents of which have finite density

Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 277–280

Article (Ukrainian)

### Conditions for solvability for analytic functions in a Dirichlet series in the half-plane

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 28–34

Article (Ukrainian)

### Representation of analytic functions by Dirichlet series in infinite closed convex polygonal domains

Ukr. Mat. Zh. - 1982. - 34, № 4. - pp. 509 — 511

Article (Ukrainian)

### Representation of analytic function by Dirichlet series in infinite convex domains

Ukr. Mat. Zh. - 1981. - 33, № 2. - pp. 244–248

Article (Ukrainian)

### The behavior of a Dirichlet series on the boundary of a region of convergence

Ukr. Mat. Zh. - 1975. - 27, № 2. - pp. 234–240