${\Bbb C}^n$中双球相交域上的奇异积分方程

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 18-25.

${\Bbb C}^n$中双球相交域上的奇异积分方程

龚定东^1,*(),郭玉琴²

¹ 浙江理工大学数学科学系杭州 310018
² 浙江理工大学图书馆杭州 310018

收稿日期:2021-06-08 出版日期:2022-02-01 发布日期:2022-02-23
通讯作者: 龚定东 E-mail:ddgong@zstu.edu.cn; ddgong2006@163.com
基金资助:
国家自然科学基金(11771400)

The Singular Integral Equations on the Intersection of Two Balls in ${\Bbb C}^n$

Dingdong Gong^1,*(),Yuqin Guo²

¹ Department of Mathematical Sciences, Zhejiang Sci-Tech University, Hangzhou 310018
² Library, Zhejiang Sci-Tech University, Hangzhou 310018

Received:2021-06-08 Online:2022-02-01 Published:2022-02-23
Contact: Dingdong Gong E-mail:ddgong@zstu.edu.cn; ddgong2006@163.com
Supported by:
the NSFC(11771400)

摘要/Abstract

摘要：

${\Bbb C}^n $中双球相交域上具有全纯核的奇异积分的Sokhotsky-Plemelj公式具有一种特殊的形式，它在边界上是分片连续的.利用这个Sokhotsky-Plemelj公式，在适当条件下得到了一个特殊的合成公式，并得到了常系数奇异积分方程和方程组的特征方程一个直接解，并把常系数奇异积分方程和方程组化为一类与之等价的Fredholm型方程和方程组.

关键词: 复双球相交域, 合成公式, 奇异积分方程, 奇异积分方程组

Abstract:

The Sokhotsky-Plemelj formula with holomorphic kernel on the intersection of two balls in $ {\Bbb C}^n$ has a special form, which is piecewise continuous on the boundary. By using this Sokhotsky-Plemelj formula the authors obtain a special composition formula, and get direct solutions to the characteristic equation of the singular integral equation and the system of the singular integral equations with constant coefficients, and convert the general singular integral equation and the system of the singular integral equations with constant coefficients to a Fredholm type equation and a system of equations which are equivalent to them.

Key words: Intersection of two balls in ${\Bbb C}^n$, Composition formula, Singular integral equation, System of the singular integral equations

中图分类号:

O174.56

龚定东,郭玉琴. ${\Bbb C}^n$中双球相交域上的奇异积分方程[J]. 数学物理学报, 2022, 42(1): 18-25.

Dingdong Gong,Yuqin Guo. The Singular Integral Equations on the Intersection of Two Balls in ${\Bbb C}^n$[J]. Acta mathematica scientia,Series A, 2022, 42(1): 18-25.

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