An abstract approach to Bohr's phenomenon

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Aizenberg L., Aytuna A., Djakov P.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.128, no.9, pp.2611-2619, 2000 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 128 Issue: 9
  • Publication Date: 2000
  • Doi Number: 10.1090/s0002-9939-00-05270-9
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2611-2619
  • Keywords: spaces of holomorphic functions, Bohr phenomenon
  • Middle East Technical University Affiliated: No

Abstract

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.