TY - JOUR

T1 - An abstract approach to bohr's phenomenon

AU - Aizenberg, L.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Bohr phenomenon

KW - Spaces of holomorphic functions

UR - http://www.scopus.com/inward/record.url?scp=23044524959&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-00-05270-9

DO - 10.1090/s0002-9939-00-05270-9

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AN - SCOPUS:23044524959

SN - 0002-9939

VL - 128

SP - 2611

EP - 2619

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 9

ER -