NORMS OF MULTIPLIERS AND BEST APPROXIMATIONS OF HOLOMORPHIC FUNCTIONS OF MANY VARIABLES


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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 Cm 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 Cm.

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