The Bombieri Problem for Bounded Univalent Functions

被引：3

作者：

Gordienko, V. G. ^{[1
]}

Prokhorov, D., V ^{[1
,2
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov 410026, Russia

[2] Petrozavodsk State Univ, Petrozavodsk 185640, Russia

来源：

MATHEMATICAL NOTES | 2019年 / 105卷 / 3-4期

基金：

俄罗斯科学基金会;

关键词：

univalent function; Bombieri number; Koebe function; Pick function;

D O I：

10.1134/S0001434619030040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：342 / 350

页数：9

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[1] The Bombieri Problem for Bounded Univalent Functions
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