Authors
Rosihan M Ali, Roger W Barnard, Alexander Yu Solynin
Publication date
2017/5/1
Journal
Journal of Mathematical Analysis and Applications
Volume
449
Issue
1
Pages
154-167
Publisher
Academic Press
Description
Bohr's phenomenon, first introduced by Harald Bohr in 1914, deals with the largest radius r, 0< r< 1, such that the inequality∑ k= 0∞| a k| r k≤ 1 holds whenever the inequality|∑ k= 0∞ a k z k|≤ 1 holds for all| z|< 1. The exact value of this largest radius known as Bohr's radius, which is r b= 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 W α={w:| arg⁡ w|< π α/2}, 1≤ α≤ 2. In particular, we find Bohr's radius for this class.
Total citations
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Scholar articles
RM Ali, RW Barnard, AY Solynin - Journal of Mathematical Analysis and Applications, 2017