无穷直线上k解析函数的非正则型Riemann边值问题  

Riemann boundary value problem of non-normal type for k-analytic functions on infinite straight line

作　　者：曾伟[1] ZENG Wei(School of Preparatory Education,Southwest Minzu University,Chengdu 610041,P.R.C.)

机构地区：[1]西南民族大学预科教育学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2019年第1期95-102,共8页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：中央高校基本科研业务费专项项目(2016NZYQN42)

摘　　要：主要研究了无穷直线上的k解析函数u(z).首先给出了k解析函数的定义,并在无穷直线上定义了Cauchy型积分,同时给出了它的具体表达式.然后,提出了k解析函数在无穷直线上的非正则型的Riemann边值问题.根据解析函数的知识,分别讨论了k解析函数在齐次和非齐次这两种情况下的非正则型的Riemann边值问题,得到了边值问题的可解性条件,从而给出了所讨论边值问题的可解性定理.This paper studies the k-analytic functions on infinite straight line. First,the definition of k-analytic function is given. Then,the cauchy type integral is defined on an infinite straight line and its concrete expression is given. The Riemann boundary value problem of non-normal type for k-analytic functions on infinite straight line is studies. According to the knowledge of analytic functions,this problem is discussed in both homogeneous and inhomogeneous cases. The theorems of solvability of the problem are obtained.

关 键 词：k解析函数 非正则 无穷直线 RIEMANN边值问题 

分 类 号：O175.8[理学—数学]