复Hilbert空间单位球上一类新的Roper-Suffridge算子

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 637-646.

复Hilbert空间单位球上一类新的Roper-Suffridge算子

夏红川¹, 刘浩², 钟春平³

1 信阳师范学院数学与统计学院河南信阳 464000;
2 河南大学数学与统计学院河南开封 475001;
3 厦门大学数学科学学院福建厦门 361005

收稿日期:2016-10-21 修回日期:2017-03-17 出版日期:2017-08-26 发布日期:2017-08-26
通讯作者: 钟春平,E-mail:zcp@xmu.edu.cn E-mail:zcp@xmu.edu.cn
作者简介:夏红川,E-mail:cuttheknots@126.com;刘浩,E-mail:haoliu@henu.edu.cn;
基金资助:
国家自然科学基金（11571288，11671330，11271359，11471098）和信阳师范学院“南湖学者奖励计划”青年项目

A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces

Xia Hongchuan¹, Liu Hao², Zhong Chunping³

1 College of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000;
2 College of Mathematics and Statistics, Henan University, Henan Kaifeng 475001;
3 School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005

Received:2016-10-21 Revised:2017-03-17 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the NSFC (11571288, 11671330, 11271359, 11471098) and the Nanhu Scholars Program for Young Scholars of XYNU

摘要/Abstract

摘要：

构造了复Hilbert空间X的单位球B上一类新的Roper-Suffridge算子

其中dim X≥n，f是单位圆盘D上一个正规化局部双全纯函数，{e_j∈X，j=1，2，…n}是X中一组单位正交向量.证明当参数β_j满足一些特定条件时，该算子在单位球B上分别保持β型螺形性、α次殆星形性和α次星形性.

关键词: Roper-Suffridge算子, 双全纯映照, Hilbert空间

Abstract:

In this paper, we construct a new Roper-Suffridge extension operator

on the unit ball B in complex Hilbert space X, where dim X ≥ n, f is a normalized locally biholomorphic function on the unit disc D, {e_j∈X,j=1,2,…n} is a series of orthogonal unit vectors in X. Under some special conditions of β_j, we prove the operator can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of order α on the unit ball B, respectively.

Key words: Roper-Suffridge operator, Biholomorphic mappings, Hilbert spaces

中图分类号:

O174.56

夏红川, 刘浩, 钟春平. 复Hilbert空间单位球上一类新的Roper-Suffridge算子[J]. 数学物理学报, 2017, 37(4): 637-646.

Xia Hongchuan, Liu Hao, Zhong Chunping. A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2017, 37(4): 637-646.

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