2019
Том 71
№ 8

# Savchuk M. V.

Articles: 4
Article (Ukrainian)

### Approximation of bounded holomorphic and harmonic functions by Fejér means

Ukr. Mat. Zh. - 2019. - 71, № 4. - pp. 516-542

We compute the exact values of the exact upper bounds on the classes of bounded holomorphic and harmonic functions in a unit disk for the remainders in a Voronovskaya-type formula in the case of approximation by Fej´er means. We also present some consequences that are of independent interest.

Brief Communications (Ukrainian)

### Approximation of holomorphic functions of Zygmund class by Fejer means

Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1148-1152

We obtain an asymptotic equality for the upper bounds of deviations of Fejer means on the Zygmund class of functions holomorphic in the unit disk.

Article (Ukrainian)

### Summation of p-Faber series by the Abel–poisson method in the integral metric

Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 660–673

We establish conditions on the boundary $\Gamma$ of a bounded simply connected domain $\Omega \subset \mathbb{C}$ under which the p-Faber series of an arbitrary function from the Smirnov space ${E_p}\left( \Omega \right),1 \leqslant p < \infty$, can be summed by the Abel–Poisson method on the boundary of the domain up to the limit values of the function itself in the metric of the space ${L_p}\left( \Gamma \right)$.

Article (Ukrainian)

### Norms of Multipliers and Best Approximations of Holomorphic Functions of Many Variables

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1669-1680

We show that the Lebesgue–Landau constants of linear methods for summation of Taylor series of functions holomorphic in a polydisk and in the unit ball from $\mathbb{C}^m$ over triangular domains do not depend on the number m. On the basis of this fact, we find a relation between the complete and partial best approximations of holomorphic functions in a polydisk and in the unit ball from $\mathbb{C}^m$ .