复Hilbert空间单位球上一类新的Roper-Suffridge算子  

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

作　　者：夏红川 刘浩[2] 钟春平[3] Xia Hongchuan Liu Hao Zhong Chunping(College of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000 College of Mathematics and Statistics, Henan University, Henan Kaifeng 475001 School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005)

机构地区：[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

出　　处：《数学物理学报（A辑）》2017年第4期637-646,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(11571288;11671330;11271359;11471098);信阳师范学院"南湖学者奖励计划"青年项目~~

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.In this paper, we construct a new Roper-Suffridge extension operator Фβ1,……βn＋1f（x）（z）=F（z）=∑k=1^n（（z,e1）/f（（z,e1）βk（z,ek）ek＋（（z,e1）/（（z,e1）））^βn＋1（z-k=1^n（z,ek）ek）on the unit ball B in complex Hilbert space X, where dim X ≥ n, f is a normalized locMly biholomorphic function on the unit disc D,{ej∈X,j=1,2,…,n} is a series of orthogonal unit vectors in X. Under some special conditions of βj, we prove the operator can preserve the property of spirallikeness of type β, ahnost starlikeness of order α and starlikeness of order on the unit ball B, respectively.

关 键 词：Roper—Suffridge算子 双全纯映照 HILBERT空间 

分 类 号：O174.56[理学—数学]