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.
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
SN - 0022-247X
VL - 449
SP - 154
EP - 167
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -