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

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