非均匀解析函数与非均匀调和函数的刻画  

The characterization of heterogeneous complex analyticfunctions and heterogeneous harmonic functions

作　　者：郑允望 俞荣杰 陶继成 ZHENG Yunwang;YU Rongjie;TAO Jicheng(College of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

出　　处：《中国计量大学学报》2020年第4期531-538,共8页Journal of China University of Metrology

摘　　要：目的:研究非均匀解析函数、非均匀调和函数。方法:利用微分算子z,z-、非均匀Cauchy积分公式,讨论非均匀解析函数、非均匀调和函数性质。结果:获得了非均匀解析函数、非均匀调和函数的微分算子z,z-刻画,建立了关于非均匀调和函数的刘维尔定理、非均匀次调和函数的性质。结论:非均匀复数域空间上的非均匀解析函数、非均匀调和函数和非均匀次调和函数,与复数域空间上的解析函数、调和函数和次调和函数有类似的性质。Aims:This paper aims to study the heterogeneous analytic functions and the heterogeneous harmonic functions.Methods:Using differential operators z,z-and the heterogeneous Cauchy integral formula,we discussed the properties of the heterogeneous analytic functions and the heterogeneous harmonic functions.Results:We obtained the characterizations of the differential operators z,z-on the heterogeneous analytic functions and the heterogeneous harmonic functions,established the heterogeneous Liouville s theorem of the heterogeneous harmonic function,and then obtained some properties of the heterogeneous subharmonic function.Conclusions:The heterogeneous analytic functions,heterogeneous harmonic functions and heterogeneous subharmonic functions in heterogeneous complex spaces have similar properties to analytic functions,harmonic functions and subharmonic functions in complex spaces.

关 键 词：非均匀偏微分算子 非均匀调和函数 最大模原理 非均匀次调和函数 

分 类 号：O174.5[理学—数学]