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An abstract approach to Bohr's phenomenon
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Date
2000-01-01
Author
Aizenberg, L
Aytuna, A
Djakov, P
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In 1914 Bohr discovered that there exists r is an element of (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.
Subject Keywords
Applied Mathematics
,
General Mathematics
URI
https://hdl.handle.net/11511/66335
Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
DOI
https://doi.org/10.1090/s0002-9939-00-05270-9
Collections
Department of Mathematics, Article
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L. Aizenberg, A. Aytuna, and P. Djakov, “An abstract approach to Bohr’s phenomenon,”
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
, pp. 2611–2619, 2000, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66335.