An abstract approach to bohr's phenomenon

L. Aizenberg

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

In 1914 Bohr discovered that there exists r ∈ (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.

Original languageEnglish
Pages (from-to)2611-2619
Number of pages9
JournalProceedings of the American Mathematical Society
Volume128
Issue number9
DOIs
StatePublished - 2000

Keywords

  • Bohr phenomenon
  • Spaces of holomorphic functions

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