An abstract approach to Bohr’s phenomenon
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- by L. Aizenberg, A. Aytuna and P. Djakov PDF
- Proc. Amer. Math. Soc. 128 (2000), 2611-2619 Request permission
Abstract:
In 1914 Bohr discovered that there exists $r \in (0,1)$ such that if a power series converges in the unit disk and its sum has modulus less than $1$, then for $|z| < r$ the sum of absolute values of its terms is again less than $1$. Recently analogous results were obtained for functions of several variables. Our aim here is to present an abstract approach to the problem and show that Bohr’s phenomenon occurs under very general conditions.References
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Additional Information
- L. Aizenberg
- Affiliation: Department of Mathematics and Computer Science, Bar-Ilan University, 52900Ramat-Gan, Israel
- Email: aizenbrg@macs.biu.ac.il
- A. Aytuna
- Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
- MR Author ID: 28620
- Email: aytuna@rorqual.cc.metu.edu.tr
- P. Djakov
- Affiliation: Department of Mathematics, Sofia University, 1164 Sofia, Bulgaria
- Email: djakov@fmi.uni-sofia.bg
- Received by editor(s): July 17, 1998
- Received by editor(s) in revised form: October 15, 1998
- Published electronically: March 1, 2000
- Additional Notes: The first author’s research was supported by the BSF grant No 94-00113
The second author wishes to thank L. Aizenberg and institute E. Noether for the invitation to Bar-Ilan University and their hospitality during his visit in Israel
The third author’s research was supported in part by NRF of Bulgaria, grant no. MM-808/98 - Communicated by: Steven R. Bell
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2611-2619
- MSC (2000): Primary 32A37, 32A05; Secondary 46E10
- DOI: https://doi.org/10.1090/S0002-9939-00-05270-9
- MathSciNet review: 1657738