UNIVALENCE OF HARMONIC FUNCTIONS, THE PROBLEM OF PONNUSAMY AND SAIRAM, AND CONSTRUCTIONS OF UNIVALENT POLYNOMIALS

被引：9
|
作者：
Starkov, V. V. [1 ]
机构：
[1] Petrozavodsk State Univ, 33 Lenina St, Petrozavodsk 185910, Russia
来源：
PROBLEMY ANALIZA-ISSUES OF ANALYSIS | 2014年 / 3卷 / 02期
关键词：
harmonic functions; criteria of the univalence; harmonic univalent polynomials;
D O I：
10.15393/j3.art.2014.2729
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The criterion of the univalence of a harmonic mapping is obtained in this paper. Particularly, it permits to formulate the conjecture of coincidence of the harmonic function classes S-H(0) = S-H(0)(S) (the problem of Ponnusamy and Sairam), in analytic form. The method of construction of the univalent harmonic polynomials with desired properties, according to a given harmonic function, is obtained by means of the univalence criteria.
引用
收藏
页码：59 / 73
页数：15
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