一階連續可微復值函數的開映射定理

董新漢++劉宗盛

DOI：10.7612/j.issn.10002537.2017.02.013

摘要將解析函數的保區域定理、最大模定理和惟一性定理推廣至一階連續可微的復值函數.并進一步將其拓展到高維空間.對解析函數根點的重數、曲線的index和拓撲度進行了討論和展望.

關鍵詞保區域定理；最大模定理；惟一性定理

中圖分類號G420；O1745文獻標識碼A文章編號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