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

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 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 .