2017
Том 69
№ 9

All Issues

Vynnyts’kyi B. V.

Articles: 17
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 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.

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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.

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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.

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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.

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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