The infinite range of infinite Blaschke product
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- by Xin-Han Dong, Wen-Hui Ai and Hai-Hua Wu PDF
- Proc. Amer. Math. Soc. 148 (2020), 193-201 Request permission
Abstract:
For an infinite Blaschke product $B$, does there necessarily exist $\delta >0$ such that each $w$ satisfying $|w|<\delta$ is assumed infinitely often by $B$? Stephenson raised this question in 1979 and then constructed a counterexample in 1988 to prove that the answer to his problem is negative. In this paper, we find two sufficient conditions under which the answer to the problem is positive.References
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Additional Information
- Xin-Han Dong
- Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Peoples’ Republic of China
- MR Author ID: 240828
- Email: xhdong@hunnu.edu.cn
- Wen-Hui Ai
- Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, 410082, People’s Republic of China
- Email: awhxyz123@163.com
- Hai-Hua Wu
- Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, 410082, People’s Republic of China
- Email: hunaniwa@163.com
- Received by editor(s): November 11, 2018
- Received by editor(s) in revised form: April 8, 2019
- Published electronically: July 1, 2019
- Additional Notes: The second author is the corresponding author.
This research was supported in part by the NNSF of China (Nos. 11831007, 11571099, 11701166). - Communicated by: Filippo Bracci
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 193-201
- MSC (2010): Primary 30C35; Secondary 30C55
- DOI: https://doi.org/10.1090/proc/14672
- MathSciNet review: 4042842