An abstract approach to Bohr's phenomenon

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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

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Department of Mathematics, Article

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Citation Formats

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.