2019
Том 71
№ 11

# Vynnyts’kyi B. V.

Articles: 22
Brief Communications (Russian)

### On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane

Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 851–856

We obtain the description of the zeros, singular boundary functions, and modules of angular boundary values of the functions $f \neq 0$ which are analytic in the half-plane $C_{+} = \{ z : \Re z > 0 \}$ and satisfy the condition $$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 ) (\forall z \in \mathbb{Ñ}_{+} ): | f ( z ) | \leq c_1 \exp ( (\sigma + \varepsilon) | z \eta ( | z | ) ),$$, where $0 \leq \sigma < +\infty$ is a given number and $\eta$ is a positive function continuously differentiable on $[0; +\infty$ and such that $t\eta'(t)/\eta(t) \rightarrow 0$ as $t \rightarrow + \infty$/

Brief Communications (Ukrainian)

### Interpolation Sequences for the Class of Functions of Finite η-Type Analytic in the Unit Disk

Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 425-430

We establish conditions for the existence of a solution of the interpolation problem f n ) = b n in the class of functions f analytic in the unit disk and such that $$\left( {\exists \;c_1 > 0} \right)\;\left( {\forall z,\;|\;z\;| < 1} \right):\;\;\left| {f\left( z \right)} \right|\;\; \leqslant \;\;\;\exp \left( {c_1 \eta \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right).$$ Here, η : [1; +∞) → (0; +∞) is an increasing function convex with respect to ln t on the interval [1; +∞) and such that ln t = o(η(t)), t → ∞.

Brief Communications (Ukrainian)

### On Zeros of One Class of Functions Analytic in a Half-Plane

Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1254-1259

We describe sequences of zeros of functions f ≢ 0 analytic in the half-plane ${\mathbb{C}}_ + = \{ z:\operatorname{Re} z >0\}$ and satisfying the condition $(\exists {\tau}_1 \in (0;1))(\exists c_1 >0)(\forall z \in {\mathbb{C}}_ + ):|f(z)| \leqslant c_1 \exp ({\eta}^{\tau }_1 (c_1 |z|)),$ where η: [0; +∞) → (0; +∞) is an increasing function such that the function ln η(r) is convex with respect to ln r on [1; +∞).

Article (Ukrainian)

### On Interpolation Sequences of One Class of Functions Analytic in the Unit Disk

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 879-886

We establish a criterion for the existence of a solution of the interpolation problem f n ) = b n in the class of functions f analytic in the unit disk and satisfying the relation $$\left( {\exists {\tau }_{1} \in \left( {0;1} \right)} \right)\;\left( {\exists c_1 >0} \right)\;\left( {\forall z,\left| z \right| < 1} \right):\;\left| {f\left( z \right)} \right| \leqslant \exp \left( {c_1 \gamma ^{{\tau }_{1} } \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right),$$ where γ: [1; +∞) → (0; +∞) is an increasing function such that the function lnγ(t) is convex with respect to lnt on the interval [1; +∞) and lnt = o(lnγ(t)), t → ∞.

Article (Ukrainian)

### A Remark on the Completeness of Systems of Exponentials with Weight in $L^2(ℝ)$

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 875-880

We establish new conditions for the completeness of systems of exponentials with weight in L 2(ℝ), which complement and generalize the results obtained earlier by the authors.

Article (Ukrainian)

### On zeros of functions of given proximate formal order analytic in a half-plane

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 904–909

We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$ where 0≤σ<+∞ and η is a positive function continuously differentiable on [0; +∞) and such thatxη′(x)/η(x)→0 asx→+∞.

Article (Ukrainian)

### Description of sequences of zeros of one class of functions analytic in a half-plane

Ukr. Mat. Zh. - 1998. - 50, № 9. - pp. 1169–1176

We describe sequences of zeros of functions ƒ ≠ 0 that are analytic in the right half-plane and satisfy the condition ¦ƒ(z)¦ ≤ 0(1) exp (σ¦ z ¦η(¦ z ¦)), 0 ≤ <+ ∞, Re z > 0, where η: [0; + ∞) → (- ∞; + ∞) is a function of bounded variation.

Article (Ukrainian)

### On the growth of functions represented by Dirichlet series with complex coefficients on the real axis

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1610–1616. December

We establish conditions under which, for a Dirichlet series $F(z) = \sum_{n = 1}^{∞} d n \exp(λ_n z)$, the inequality $⋎F(x)⋎ ≤ y(x),\quad x ≥ x_0$, implies the relation $\sum_{n = 1}^{∞} |d_n \exp(λ_n z)| ⪯ γ((1 + o(1))x)$ as $x → +∞$, where $γ$ is a nondecreasing function on $(−∞,+∞)$.

Article (Russian)

### Approximation properties of systems of exponentials in one space of analytic functions

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 168-183

We obtain a criterion of completeness of a system of exponentials in the Hardy-Smirnov spaces in unbounded convex polygons and study the properties of incomplete systems of exponentials.

Article (Russian)

### On zeros of functions analytic in a half plane and completeness of systems of exponents

Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 484–500

Sequences of zeros are described for functions $f$ analytic in the right halfplanc and satisfying the condition $|f(z)| \leq 0(1) \exp (\sigma|z|),\quad 0 \leq \sigma \leq \infty$ criterion of completeness of a system of exponentials in a space of functions analytic in a semistrip is established.

Article (Ukrainian)

### Behavior on the real line of entire functions represented by Dirichlet series

Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 265–269

Article (Ukrainian)

### Completeness of systems of exponentials with weight

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1695–1700

Article (Ukrainian)

### Construction of entire function of arbitrary order with given asymptotic properties

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 143–148

Article (Ukrainian)

### A description of certain absolutely representing systems

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 93–95

Article (Ukrainian)

### Completeness of the system {f(?nz)}

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 655–658

Article (Ukrainian)

### Conditions for the convergence of sequences in certain spaces of analytic functions

Ukr. Mat. Zh. - 1982. - 34, № 6. - pp. 741—744

Article (Ukrainian)

### Representation of analytic functions by series $\sum_{n = 1}^\infty {d_n f(\lambda _n z)}$

Ukr. Mat. Zh. - 1979. - 31, № 6. - pp. 650– 657

Article (Ukrainian)

### Growth of entire functions defined by series $\sum_{n = 1}^\infty {d_n f(\lambda _n z)}$

Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 537–540

Article (Ukrainian)

### Representation of functions by series $\sum_{n = 1}^\infty {d_n } f(\lambda _n z)$

Ukr. Mat. Zh. - 1979. - 31, № 3. - pp. 256–265

Article (Ukrainian)

### Coefficients of dirichlet series specifying an entire function

Ukr. Mat. Zh. - 1977. - 29, № 2. - pp. 232–237

Article (Ukrainian)

### On derivatives of entire functions

Ukr. Mat. Zh. - 1975. - 27, № 4. - pp. 443–451

Article (Ukrainian)

### Asymptotic properties of the coefficients of Dirichlet series representing entire functions

Ukr. Mat. Zh. - 1975. - 27, № 2. - pp. 147–157