Qualitative Results in the Bombieri Problem for Conformal Mappings
- Autores: Prokhorov D.1,2
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Afiliações:
- Department of Mathematics and Mechanics
- Petrozavodsk State University
- Edição: Volume 40, Nº 9 (2019)
- Páginas: 1397-1409
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205551
- DOI: https://doi.org/10.1134/S1995080219090178
- ID: 205551
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Resumo
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.
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Sobre autores
D. Prokhorov
Department of Mathematics and Mechanics; Petrozavodsk State University
Autor responsável pela correspondência
Email: ProkhorovDV@info.sgu.ru
Rússia, Saratov, 410012; Petrozavodsk, Republic of Karelia, 185910