TY - JOUR

T1 - A note on Bohr's phenomenon for power series

AU - Ali, Rosihan M.

AU - Barnard, Roger W.

AU - Solynin, Alexander Yu

N1 - Publisher Copyright:
© 2016 Elsevier Inc.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Bohr's phenomenon, first introduced by Harald Bohr in 1914, deals with the largest radius r, 0k=0∞|ak|rk≤1 holds whenever the inequality |∑k=0∞akzk|≤1 holds for all |z|<1. The exact value of this largest radius known as Bohr's radius, which is rb=1/3, was discovered long ago. In this paper, we first discuss Bohr's phenomenon for the classes of even and odd analytic functions and for alternating series. Then we discuss Bohr's phenomenon for the class of analytic functions from the unit disk into the wedge domain Wα={w:|argw|<πα/2}, 1≤α≤2. In particular, we find Bohr's radius for this class.

AB - Bohr's phenomenon, first introduced by Harald Bohr in 1914, deals with the largest radius r, 0k=0∞|ak|rk≤1 holds whenever the inequality |∑k=0∞akzk|≤1 holds for all |z|<1. The exact value of this largest radius known as Bohr's radius, which is rb=1/3, was discovered long ago. In this paper, we first discuss Bohr's phenomenon for the classes of even and odd analytic functions and for alternating series. Then we discuss Bohr's phenomenon for the class of analytic functions from the unit disk into the wedge domain Wα={w:|argw|<πα/2}, 1≤α≤2. In particular, we find Bohr's radius for this class.

KW - Analytic function

KW - Bohr's radius

UR - http://www.scopus.com/inward/record.url?scp=85008199890&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.11.049

DO - 10.1016/j.jmaa.2016.11.049

M3 - Article

AN - SCOPUS:85008199890

VL - 449

SP - 154

EP - 167

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -