复HILBERT空间单位球上的零伦全纯映照  

Null-homotopic holomorphic mappings on unit ball in Hilbert space

作　　者：刘爱超[1] 崔艳艳[2] 刘浩[3] 

机构地区：[1]黄淮学院数学系,河南驻马店463000 [2]周口师范学院数学与信息科学系,河南周口466000 [3]河南大学数学与信息科学学院,河南开封475004

出　　处：《兰州理工大学学报》2014年第4期150-154,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11271359);河南省教育厅科学技术研究重点项目(14B110015)

摘　　要：星形映照与螺形映照是多复变几何函数论中较早被研究的两种映照,在众多映照的性质研究中起着非常重要的作用.以复分析为主要研究工具,结合拓扑学中同伦的概念,提出复Hilbert空间单位球上解析同伦和零伦的概念,并得到零伦全纯映照的判别方法.同时从同伦的观点也得到星形映照和螺形映照的一些判别方法,这些判别方法与已知的一些结论是一致的.又复欧式空间为复无限维Hilbert空间的一个特例,因此所得结果对复欧式空间中的单位球也是成立的,推广一些已知的结论.Starlike mapping and spiral-like mappings are two mappings studied earlier in geometric functions theory of multi-complex variables, playing a very important role in many mapping property researches. Using complex analysis as the main research tool and combining the concept of homotopy in topology, the concepts of analytic homotopy and nullhomotopy on unit ball in complex Hilbert space are presented and the discrimination method of null-homotopic holomorphic mappings is obtained. Meantime from the point of view of homotopy, some discrimination methods of starlike mapping and spiral-like mappings may also be deduced, which are consistent with some known conclusions. In addition, complex Euclidean space is a special case of the complex infinite dimensional Hilbert space, so that the results for unit ball in complex Euclidean space are also true and some known results are generalized.

关 键 词：星形映照 螺形映照 零伦全纯映照 

分 类 号：O174.5[理学—数学]