双曲线上的Cauchy型积分的性质  

Properties of Cauchy integral on the Hyperbola

作　　者：魏雨秋 刘华[1] WEI Yuqiu;LIU Hua(Department of Mathematics,Tianjin University of Technology and Education,Tianjin 300222)

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《宁夏师范学院学报》2023年第1期5-12,共8页Journal of Ningxia Normal University

基　　金：Natural Science Foundation of Ningxia Hui Autonomous Region (2021AAC03028)。

摘　　要：引入双曲线上的Cauchy型积分的性质问题.首先提出了沿双曲线剖开的复平面上的分区全纯函数在无穷远点处的主部与阶的定义,接着讨论了双曲线上无穷远处的Cauchy积分的性质以及双曲线上的Plemelj公式,最后讨论了Cauchy主值积分的H lder连续性.The properties of Cauchy integral on the Hyperbola are introduced.Firstly,the definition of the principal part and order of the sectionally holomorphic function at infinity on the complex plane opened along the Hyperbola is presented.Then the properties of the Cauchy integral at infinity and the Plemelj formula on the Hyperbola are discussed.Finally,the H lder continuity of the Cauchy integral with principal value is discussed.

关 键 词：双曲线 广义主部 PLEMELJ公式 

分 类 号：O175.8[理学—数学]