2019
Том 71
№ 4

All Issues

Koval’chuk Yu. A.

Articles: 3
Article (Ukrainian)

On the regularity of the growth of the modulus and argument of an entire function in the metric of $L^p [0, 2π]$

Kalinets R. Z., Koval’chuk Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 889-896

Under sufficiently general assumptions, we describe sets of entire functions $f$, sets of growing functions $λ$, and sets of complex-valued functions $H$ from $L^p [0, 2π]$, $p ∈ [1, + ∞]$, for which $$\left\{ {\frac{1}{{2\pi }}\int\limits_0^{2\pi } {|\log f(re^{i\theta } ) - \lambda (r)H(\theta )|^p } d\theta } \right\}^{1/p} = o(\lambda (r)),r \to \infty.$$

Article (Russian)

Boundary-value problems with random initial conditions and functional series from subφ (Ω). II

Koval’chuk Yu. A., Kozachenko Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 897–906

We study conditions for convergence and the rate of convergence of random functional series from the space subφ(Ω) in various norms. The results obtained are applied to the investigation of a boundary-value problem for a hyperbolic equation with random initial conditions.

Article (Russian)

Boundary-Value problems with random initial conditions and functional series from subφ (Ω). I

Koval’chuk Yu. A., Kozachenko Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 504–515

We study conditions for convergence and the rate of convergence of random functional series from the space subφ (Ω) in various norms. The results are applied to the investigation of a boundary-value problem for a hyperbolic equation with random initial conditions.