一阶连续可微复值函数的开映射定理
2017-06-02 10:39董新汉刘宗盛
湖南师范大学学报·自然科学版 2017年2期
董新汉++刘宗盛
DOI：10.7612/j.issn.10002537.2017.02.013
摘要將解析函数的保区域定理、最大模定理和惟一性定理推广至一阶连续可微的复值函数.并进一步将其拓展到高维空间.对解析函数根点的重数、曲线的index和拓扑度进行了讨论和展望.
关键词保区域定理；最大模定理；惟一性定理
中图分类号G420；O1745文献标识码A文章编号10002537（2017）02008104
On Open Mapping Theorem of Complex Valued Functions with C1 Condition
DONG Xinhan， LIU Zongsheng*
（College of Mathematics and Computer Science， Hunan Normal University， Changsha 410081， China）
AbstractThe open mapping theorem， the maximum modulus theorem and the uniqueness theorem are generalized from analytic functions to complex valued functions with C1 condition. Furthermore， the same results in highdimensional space are established， the applications of the multiplicity of root， index and degree are discussed.
Key wordsopen mapping theorem； maximum modulus theorem； uniqueness theorem
