Multidimensional analogues of Bohr's theorem on power series
Complex Variables
2007-05-23 v1
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}.
Keywords
Cite
@article{arxiv.math/9804102,
title = {Multidimensional analogues of Bohr's theorem on power series},
author = {Lev Aizenberg},
journal= {arXiv preprint arXiv:math/9804102},
year = {2007}
}
Comments
11 pages, LaTeX