Multidimensional analogues of Bohr's theorem on power series

被引：129

作者：

Aizenberg, L ^{[1
]}

机构：

[1] Bar Ilan Univ, Dept Math & Comp Sci, IL-52900 Ramat Gan, Israel

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 04期

关键词：

D O I：

10.1090/S0002-9939-99-05084-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Generalizing the classical result of Bohr, we show that if an n-variable 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 r = 1 - [GRAPHICS] This constant is near to the best one for the domain D = {z : \z(1)\ + ... + \z(n)\ < 1}.

引用

页码：1147 / 1155

页数：9