Multidimensional analogues of Bohr's theorem on power series

Lev Aizenberg

doi:10.1090/S0002-9939-99-05084-4

Multidimensional analogues of Bohr's theorem on power series

Lev Aizenberg

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

140 Scopus citations

Abstract

Generalizing the classical result of Bohr, we show that if an nvariable power series converges in n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the modulii of the terms is less than 1 in the homothetic domain r = D, where (Formula Presented). This constant is near to the best one for the domain D = (z: z₁ + … + z_n 1).

Original language	English
Pages (from-to)	1147-1155
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	128
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-99-05084-4
State	Published - 1999

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AB - Generalizing the classical result of Bohr, we show that if an nvariable power series converges in n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the modulii of the terms is less than 1 in the homothetic domain r = D, where (Formula Presented). This constant is near to the best one for the domain D = (z: z1 + … + zn 1).

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Multidimensional analogues of Bohr's theorem on power series

Abstract

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