一階連續(xù)可微復(fù)值函數(shù)的開映射定理
2017-06-02 10:39董新漢劉宗盛
湖南師范大學(xué)學(xué)報·自然科學(xué)版 2017年2期
董新漢++劉宗盛
DOI：10.7612/j.issn.10002537.2017.02.013
摘要將解析函數(shù)的保區(qū)域定理、最大模定理和惟一性定理推廣至一階連續(xù)可微的復(fù)值函數(shù).并進一步將其拓展到高維空間.對解析函數(shù)根點的重數(shù)、曲線的index和拓?fù)涠冗M行了討論和展望.
關(guān)鍵詞保區(qū)域定理；最大模定理；惟一性定理
中圖分類號G420；O1745文獻標(biāo)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
