Bohr’s power series theorem in several variables
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- by Harold P. Boas and Dmitry Khavinson PDF
- Proc. Amer. Math. Soc. 125 (1997), 2975-2979 Request permission
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 $1/(3\sqrt n )$.References
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Additional Information
- Harold P. Boas
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
- MR Author ID: 38310
- ORCID: 0000-0002-5031-3414
- Email: boas@math.tamu.edu
- Dmitry Khavinson
- Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 101045
- Email: dmitry@comp.uark.edu
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2975-2979
- MSC (1991): Primary 32A05
- DOI: https://doi.org/10.1090/S0002-9939-97-04270-6
- MathSciNet review: 1443371