Qualitative Results in the Bombieri Problem for Conformal Mappings
- 作者: Prokhorov D.1,2
-
隶属关系:
- Department of Mathematics and Mechanics
- Petrozavodsk State University
- 期: 卷 40, 编号 9 (2019)
- 页面: 1397-1409
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205551
- DOI: https://doi.org/10.1134/S1995080219090178
- ID: 205551
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详细
Bombieri’s numbers σmn characterize a behavior of the coefficient body for the class S of all holomorphic and univalent functions f in the unit disk normalized by f(z) = z + a2z2 + …. The number σmn is the limit of ratio for Re(n − an) and Re (m − am) as f tends to the Koebe function K(z) = z(1 − z)−2. It is showed in the paper that Bombieri’s conjecture about explicit values of σmn implies a sliding regime in an associated control theory problem generated by the Loewner differential equation. We develop also an asymptotical approach in verification of necessary criteria for Bombieri’s conjecture.
作者简介
D. Prokhorov
Department of Mathematics and Mechanics; Petrozavodsk State University
编辑信件的主要联系方式.
Email: ProkhorovDV@info.sgu.ru
俄罗斯联邦, Saratov, 410012; Petrozavodsk, Republic of Karelia, 185910