Clifford分析中一类新型全纯函数的性质  

Some Properties of a New Class of Holomorphic Functions in Clifford Analysis

作　　者：李尊凤[1,2] 乔玉英[1] LI Zun-feng1,2, QIAO Yu-ying1(1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China;2. School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050024, Chin)

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024 [2]河北科技大学理学院,河北石家庄050018

出　　处：《数学的实践与认识》2018年第14期293-297,共5页Mathematics in Practice and Theory

基　　金：2017年河北省研究生创新资助项目(CXZZBS2017085);国家自然科学基金(11571089);河北省自然科学基金(A2016205218,A2015205012)

摘　　要：在解析函数列的收敛性定理的基础上，讨论了Clifford分析中一类新型全纯函数（即片正则函数）的性质，如等度连续性、列紧性、内闭一致收敛性等，并且揭示了这些性质之间的内在联系．这些性质刻划了实Clifford分析中片正则函数列的基本特征，是研究其它相关性质的理论基础，从这些性质也可以看出片正则函数是一类与单复分析中全纯函数非常类似的函数类．On the basis of the convergence theorem for the analytical function sequence, in Clifford analysis, we discussed some properties of the slice monogenic function sequence, such as equicontinuity, sequential compactness, inner closed uniform convergence. And reveal the internal relations between these properties. These properties characterize the basic features of the slice monogenic function sequence and lay a theoretical foundation for studying other related properties. From these properties, we can see that the slice monogenic function is very similar to the complex analysis of one variable.

关 键 词：片正则函数 等度连续性 列紧性 内闭一致收敛 

分 类 号：O174[理学—数学]