2017
Том 69
№ 9

All Issues

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

Savchuk M. V., Savchuk V. V.

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Abstract

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

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 12, pp 2025-2037.

Citation Example: Savchuk M. V., Savchuk V. V. Norms of Multipliers and Best Approximations of Holomorphic Functions of Many Variables // Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1669-1680.

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