Clifford分析中双正则函数及调和函数在平面上的积分表示（英文）  

INTEGRAL REPRESENTATIONS FOR BI-REGULAR FUNCTIONS AND HARMONIC FUNCTIONS OVER PLANE IN CLIFFORD ANALYSIS

作　　者：张忠祥[1] 高明凤 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2016年第2期267-276,共10页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11471250)

摘　　要：本文研究了取值在Clifford代数上双正则函数及调和函数在超复平面上积分表示的问题.利用构造核函数的方法,获得了双正则函数及调和函数在超复平面上的积分表示公式,这些结果推广了Clifford分析中正则函数在超复平面上的积分表示公式.In this article, we study the integral representations over hyper-complex plane Π for bi-regular functions and harmonic functions with values in a Clifford algebra. By constructing the kernel functions, we give the integral representation formulas over hyper-complex plane Π for bi-regular functions and harmonic functions with values in a Clifford algebra. These results are extensions of integral representations over hyper-complex plane Π for regular functions.

关 键 词：CLIFFORD代数 积分表示 双正则函数 调和函数 

分 类 号：O175.5[理学—数学]