具x/ζ型卷积核的奇异积分方程的求解  

The Solution of Singular Integral Equation of the Type x/ζ of Convolution Kernel

作　　者：罗英语[1] LUO Ying-yu(School of Mathematics, Changchun Normal University, Changchun 130032, China)

机构地区：[1]长春师范大学数学学院,吉林长春130032

出　　处：《数学的实践与认识》2016年第21期223-230,共8页Mathematics in Practice and Theory

基　　金：吉林省教育厅科学技术研究项目(吉教科合字2015第356号)

摘　　要：讨论了具x/ζ型卷积核的奇异积分方程的求解问题.通过Fourier积分变换,将所讨论的积分方程转化成在一定可解条件下与其同解意义下等价的Riemann边值问题.利用Riemann边值问题理论,分别讨论了在正则和非正则两种情况下的Riemann边值问题,进而得到相对应的x/ζ变量比型卷积核的积分方程一般解及可解条件.By Fourier Integral transformation, the integral equation can be converted Rie mann boundary value problems under certain conditions, with the same solution of bound- ary value problems of equivalent. Using Riemann Boundary Value Problems theory, the two situations are discussed under the Riemann Boundary Value Problems in the regular and non-regular, and then get the corresponding type x/ζ convolution integral equations regular and non-regular type general solution and solvability condition.

关 键 词：卷积核 奇异核 正则型 非正则型 RIEMANN边值问题 

分 类 号：O175.5[理学—数学]