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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multidimensional analogues of Bohr's theorem
on power series


Author: Lev Aizenberg
Journal: Proc. Amer. Math. Soc. 128 (2000), 1147-1155
MSC (1991): Primary 32A05
Published electronically: August 5, 1999
MathSciNet review: 1636918
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Abstract: 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 $r \cdot D$, where $r = 1- \sqrt[n]{2/3}$. This constant is near to the best one for the domain $ D = \{z: |z_1 |+ \ldots + |z_n |$ $ < 1 \} .$


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Additional Information

Lev Aizenberg
Email: aizenbrg@macs.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05084-4
PII: S 0002-9939(99)05084-4
Received by editor(s): April 28, 1998
Received by editor(s) in revised form: June 8, 1998
Published electronically: August 5, 1999
Additional Notes: This work was supported by the BSF, grant No 94-00113.
Communicated by: Steven R. Bell
Article copyright: © Copyright 2000 American Mathematical Society