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 \(\mathbb{C}^m\).
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Savchuk, V.V., Savchuk, M.V. Norms of Multipliers and Best Approximations of Holomorphic Functions of Many Variables. Ukrainian Mathematical Journal 54, 2025–2037 (2002). https://doi.org/10.1023/A:1024029516357
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DOI: https://doi.org/10.1023/A:1024029516357