2018
Том 70
№ 5

All Issues

Vynnyts’kyi B. V.

Articles: 19
Brief Communications (Russian)

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

Sharan V.L., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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

Sheparovych I. B., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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

Sharan V.L., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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

Sheparovych I. B., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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 $L^2(ℝ)$

Shapovalovskii A. V., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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

Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

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

Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

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

Sequences of zeros are described for functionsf, which, in the right half plane, are analytic and satisfy the condition ¦f(z)¦?0(1) exp (?¦z¦), 0??

Article (Ukrainian)

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

Sorokivskii V. M., Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

Completeness of systems of exponentials with weight

Shapovalovskii A. V., Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

Construction of entire function of arbitrary order with given asymptotic properties

Vynnyts’kyi B. V.

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

Article (Ukrainian)

A description of certain absolutely representing systems

Vynnyts’kyi B. V.

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

Article (Ukrainian)

Completeness of the system {f(?nz)}

Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Vynnyts’kyi B. V.

Full text (.pdf)

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

Article (Ukrainian)

Coefficients of dirichlet series specifying an entire function

Vynnyts’kyi B. V.

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

Article (Ukrainian)

On derivatives of entire functions

Vynnyts’kyi B. V.

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

Article (Ukrainian)

Asymptotic properties of the coefficients of Dirichlet series representing entire functions

Vynnyts’kyi B. V.

Full text (.pdf)

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