Multidimensional analogues of Bohr's theorem on power series

Authors
Aizenberg, L
Citation
L. Aizenberg, Multidimensional analogues of Bohr's theorem on power series, P AM MATH S, 128(4), 2000, pp. 1147-1155
Citations number
7
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
128
Issue
4
Year of publication
2000
Pages
1147 - 1155
Database
ISI
SICI code
0002-9939(2000)128:4<1147:MAOBTO>2.0.ZU;2-L
Abstract
Generalizing the classical result of Bohr, we show that if an n-variable po wer series converges in n-circular bounded complete domain D and its sum ha s modulus less than 1, then the sum of the maximum of the modulii of the te rms 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}.