Univalent Subordination Chains in Reflexive Complex Banach Spaces

被引:13
作者
Graham, Ian [1 ]
Hamada, Hidetaka [1 ]
Kohr, Gabriela [1 ]
Kohr, Mirela [1 ]
机构
[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源
COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS V | 2013年 / 591卷
关键词
A-normalized univalent subordination chain; A-parametric representation; Loewner differential equation; reflexive complex Banach space; spirallike mapping; starlike mapping; transition mapping; univalent mapping; PARAMETRIC REPRESENTATION; HOLOMORPHIC-FUNCTIONS; SPIRALLIKE MAPPINGS; EVOLUTION FAMILIES; LOEWNER EQUATION; SEMIGROUPS;
D O I
10.1090/conm/591/11829
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we consider univalent subordination chains in reflexive complex Banach spaces, allowing the chains to be normalized in terms of a positive linear operator. Related adaptations in the generalized Loewner differential equation and in the notion of parametric representation are also considered. The results in this paper are generalizations to reflexive complex Banach spaces of classical and recent results in the theory of Loewner chains and the Loewner differential equation on the unit ball in C-n. Finally, we conclude with certain open problems and conjectures.
引用
收藏
页码:83 / 111
页数:29
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