2019
Том 71
№ 5

All Issues

Savchuk M. V.

Articles: 4
Article (Ukrainian)

Approximation of bounded holomorphic and harmonic functions by Fejér means

Chaichenko S. O., Savchuk M. V., Savchuk V. V.

↓ Abstract

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

Savchuk M. V., Savchuk V. V.

↓ Abstract   |   Full text (.pdf)

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

Savchuk M. V., Savchuk V. V.

↓ Abstract   |   Full text (.pdf)

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

Savchuk M. V., Savchuk V. V.

↓ Abstract   |   Full text (.pdf)

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 \(\mathbb{C}^m\) .