| 崔艳艳,王朝君,刘浩.推广的Roper-Suffridge算子与Loewner链[J].数学年刊A辑,2017,38(2):159~176 |
| 推广的Roper-Suffridge算子与Loewner链 |
| The Generalized Roper-Suffridge Operator and Loewner Chains |
| Received:June 23, 2015 Revised:January 01, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0013 |
| 中文关键词: Spirallike mappings, Loewner chains, Roper-Suffridge operator |
| 英文关键词:Spirallike mappings, Loewner chains, Roper-Suffridge operator |
| 基金项目:本文受到国家自然科学基金(No.11271359,No.U1204618)和河南省教育厅科学技术研究重点项目(No.17A110041)的资助. |
| Author Name | Affiliation | E-mail | | CUI Yanyan | College of Mathematics and Statistics, Zhoukou NormalUniversity, Zhoukou 466001, Henan, China. | cui9907081@163.com | | WANG Chaojun | College of Mathematics and Statistics, Zhoukou NormalUniversity, Zhoukou 466001, Henan, China. | wang9907081@163.com | | LIU Hao | Department of Mathematics, Henan University, Kaifeng 475001, Henan, China. | haoliu@henu.edu.cn |
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| 中文摘要: |
| 将Roper-Suffridge算子在$\mathbb{C}^n$中单位球$B^n$上做了进一步推广,并考察推广后的算子何时能保持双全纯映照子族的性质.
利用$k$阶零点及双全纯映照子族的增长定理, 重点研究了推广后的算子在$B^{n}$
上保持$\alpha$次$\beta$型螺形映照及强$\beta$型螺形映照的性质,
并由调和函数的最小值原理及具有正实部函数的性质, 揭示了推广后的算子能够嵌入Loewner链,从而得到推广后的算子在$B^{n}$
上保持$\alpha$次殆$\beta$型螺形映照的性质. |
| 英文摘要: |
| The authors extend the Roper-Suffridge operator to the unit ball
$B^n$ in $\mathbb{C}^n$, and seek conditions under which the
extended operator preserves the properties of subclasses of
biholomorphic mappings. By the zero of order $k$ and the growth
theorems for subclasses of biholomorphic mappings, it is primarily
studied that the extended operator preserves spirallikeness of order
$\alpha$ and type $\beta$, strong spirallikeness of type $\beta$ on
$B^{n}$. By the Minimum Principle for harmonic functions and the
property of functions which have positive real parts, the
extended operator can be embedded into a Loewner chain, and thus the extended operator preserves almost spirallikeness of type
$\beta$ and order $\alpha$ on $B^{n}$. |
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