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Multidimensional analogues of Bohr's theorem on power series

Lev Aizenberg
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Abstract

Generalizing the classical result of Bohr, we show that if an n-variable power series converges in an n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the moduli of the terms is less than 1 in the homothetic domain r*D, where r = 1 - (2/3)^(1/n). This constant is near to the best one for the domain D = {z: |z_1| + ... + |z_n| < 1}.

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Lev Aizenberg. 1998-04-21. Multidimensional analogues of Bohr's theorem on power series. https://arxiv.org/abs/math/9804102

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