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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2019, Volume 105, Issue 3, Pages 364–374 (Mi mz11804)

The Bombieri Problem for Bounded Univalent Functions

V. G. Gordienkoa, D. V. Prokhorovab

a Saratov State University
b Petrozavodsk State University

Abstract: Bombieri proposed to describe the structure of the sets of values of the initial coefficients of normalized conformal mappings of the disk in a neighborhood of the corner point corresponding to the Koebe function. The Bombieri numbers characterize the limit position of the support hyperplane passing through a critical corner point. In this paper, the Bombieri problem is studied for the class of bounded normalized conformal mappings of the disk, where the role of the Koebe function is played by the Pick function. The Bombieri numbers for a pair of two nontrivial initial coefficients are calculated.

Keywords: univalent function, Bombieri number, Koebe function, Pick function.

 Funding Agency Grant Number Russian Science Foundation 17-11-01229 The work of the second author was supported by the Russian Science Foundation under grant 17-11-01229.

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DOI: https://doi.org/10.4213/mzm11804

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UDC: 517.54

Citation: V. G. Gordienko, D. V. Prokhorov, “The Bombieri Problem for Bounded Univalent Functions”, Mat. Zametki, 105:3 (2019), 364–374

Citation in format AMSBIB
\Bibitem{GorPro19} \by V.~G.~Gordienko, D.~V.~Prokhorov \paper The Bombieri Problem for Bounded Univalent Functions \jour Mat. Zametki \yr 2019 \vol 105 \issue 3 \pages 364--374 \mathnet{http://mi.mathnet.ru/mz11804} \crossref{https://doi.org/10.4213/mzm11804} \elib{http://elibrary.ru/item.asp?id=37045121}