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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 128 Issue: 9
  • Publication Date: 2000
  • Doi Number: 10.1090/s0002-9939-00-05270-9
  • Title of Journal : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.2611-2619

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.