An abstract approach to Bohr's phenomenon


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Aizenberg L., Aytuna A., Djakov P.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.128, sa.9, ss.2611-2619, 2000 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 128 Sayı: 9
  • Basım Tarihi: 2000
  • Doi Numarası: 10.1090/s0002-9939-00-05270-9
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2611-2619
  • Anahtar Kelimeler: spaces of holomorphic functions, Bohr phenomenon
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.