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

 

Bohr's power series theorem in several variables


Authors: Harold P. Boas and Dmitry Khavinson
Journal: Proc. Amer. Math. Soc. 125 (1997), 2975-2979
MSC (1991): Primary 32A05
MathSciNet review: 1443371
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Abstract: Generalizing a classical one-variable theorem of Bohr, we show that if an $n$-variable power series has modulus less than $1$ in the unit polydisc, then the sum of the moduli of the terms is less than $1$ in the polydisc of radius $1/(3\sqrt n\,)$.


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Additional Information

Harold P. Boas
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
Email: boas@math.tamu.edu

Dmitry Khavinson
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: dmitry@comp.uark.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04270-6
PII: S 0002-9939(97)04270-6
Received by editor(s): May 8, 1996
Additional Notes: The first author’s research was supported in part by NSF grant number DMS 9500916 and in part at the Mathematical Sciences Research Institute by NSF grant number DMS 9022140.
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society