2018
Том 70
№ 8

All Issues

Zabolotskii N. V.

Articles: 10
Article (Ukrainian)

Entire functions of order zero with zeros on a logarithmic spiral

Tarasyuk S. I., Zabolotskii N. V., Zabolotskyi M. V.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 923-932

We prove the Valiron-type and Valiron – Titchmarsh-type theorems for entire functions of order zero with zeros on a logarithmic spiral.

Article (Ukrainian)

Sufficient conditions for the existence of the $\upsilon$ -density for zeros of entire function of order zero

Mostova M. R., Zabolotskii N. V.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 506-516

We select the subclasses of zero-order entire functions $f$ for which we present sufficient conditions for the existence of $\upsilon$ -density for zeros of $f$ in terms of the asymptotic behavior of the logarithmic derivative F and regular growth of the Fourier coefficients of $F$.

Article (Ukrainian)

Logarithmic Derivative and the Angular Density of Zeros for a Zero-Order Entire Function

Mostova M. R., Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 473–481

For an entire function of zero order, we establish the relationship between the angular density of zeros, the asymptotics of logarithmic derivative, and the regular growth of its Fourier coefficients.

Article (Ukrainian)

Criteria for the regularity of growth of the logarithm of modulus and the argument of an entire function

Bodnar O. V., Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 885–893

For entire functions whose zero counting functions are slowly increasing, we establish criteria for the regular growth of their logarithms of moduli and arguments in the metric of $L^p [0, 2π]$.

Brief Communications (Ukrainian)

Julia lines of entire functions of slow growth

Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 829–834

We obtain sufficient conditions under which the Julia lines of entire functions of slow growth do not have finite exceptional values.

Article (Russian)

Polynomial Asymptotics of Entire Functions of Finite Order

Borova O. I., Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 723-732

We obtain new asymptotic relations for entire functions of finite order with zeros on a ray under the condition of regular growth for the counting function of their zeros. These relations improve the well-known results of Valiron.

Brief Communications (Ukrainian)

Asymptotic Behavior of Logarithmic Potential of Zero Kind

Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 11. - pp. 1568-1574

Under a fairly general condition on the behavior of a Borel measure,we obtain unimprovable asymptotic formulas for its logarithmic potential.

Article (Ukrainian)

Asymptotics of Blaschke Products the Counting Function of Zeros of Which Is Slowly Increasing

Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 12. - pp. 1650-1660

We find the asymptotics as z→ 1 for the Blaschke product with positive zeros the counting function of which n(t) is slowly increasing, i.e., n((t+ 1)/2) ∼ n(t) as t→ 1.

Article (Ukrainian)

Asymptotics of the logarithmic derivative of an entire function of zero order

Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 32–40

We find asymptotic formulas for the logarithmic derivative of a zero-order entire functionf whose zeros have an angular density with respect to the comparison function $v(r) = r^{\lambda(r)}$, where $λ(r)$ is the zero proximate order of the counting function $n(r)$ of zeros of $f$.

Article (Ukrainian)

A generalization of the Lindelöf theorem

Sheremeta M. M., Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 9. - pp. 1177–1192

We present a generalization of the Lindelöf theorem on conditions that should be imposed on the coefficients of the Taylor series of an entire transcendental function ƒ in order that the relation \(ln M_f (r) - \tau r^\rho , r \to \infty , M_f (r) = \max \left\{ {\left| {f(r)} \right|:|z| = r} \right\}\) , be satisfied.