复Hilbert空间上的零伦全纯映照的构造  

The Construction of the Null-Homotopic Holomorphic Mapping on Hilbert Space

作　　者：刘爱超[1] 程俊芳[2] 刘浩[2] 

机构地区：[1]黄淮学院数学系,河南驻马店463000 [2]河南大学数学与信息科学学院,河南开封475004

出　　处：《中北大学学报（自然科学版）》2014年第3期233-237,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271359);河南省计划项目(112300410251)

摘　　要：在复平面上正规化零伦全纯函数的例子有很多,但在复高维空间中零伦全纯映照却较少.因而在复高维空间中构造零伦全纯映照,为其存在性提供依据,是众多研究人员工作的重点之一.以复分析为工具,将不同形式的Roper-Suffridge算子与拓扑学中同伦的概念相结合,在将同伦映照定义做适当修改后,得出利用复平面中单位圆盘上的正规化零伦全纯函数可以分别构造出复Hilbert空间单位球B和Ω(p2,…,pn+1)上的零伦映照.所得结论对复欧式空间Cn中的单位球Bn同样成立.There are many examples of the null-homotopic holomorphic function in the complex plane,but less in complex high dimensional space.Constructing null-homotopic holomorphic mapping in complex high-dimensional was one of the focus of the work for many researchers to provide the theoretical basis for its existence.Using complex analysis as a tool,and combining different forms of the RoperSuffridge operator with the concept of topology homotopy,null-homotopic holomorphic mappings respectively on the unit ball B and Ω（p2,…,pn＋1）in the complex Hilbert space could be constructed by using a normalized null-homotopic holomorphic function of the unit disc in the complex plane after suitably modification.The same conclusions are true for the unit ball in the complex euclidean space.

关 键 词：零伦全纯映照 同伦 HILBERT空间 ROPER-SUFFRIDGE算子 构造 

分 类 号：O174.5[理学—数学]