在指数增长的函数类中的奇异积分方程与Riemann边值问题  

THE SINGULAR INTEGRAL EQUATIONS IN FUNCTIONS CLASS OF EXPONENTIAL ORDER INCREASING AND RIEMANN BOUNDARY VALUE PROBLEM

作　　者：李平润[1,2] 

机构地区：[1]中国科学技术大学数学科学学院,合肥230026 [2]曲阜师范大学数学科学学院,曲阜273165

出　　处：《系统科学与数学》2015年第1期99-109,共11页Journal of Systems Science and Mathematical Sciences

摘　　要：提出并讨论了在指数增长的函数类中带有卷积核与Cauchy核的奇异积分方程,通过Fourier变换及文章所给出的引理,将奇异积分方程转化为一类推广的两条平行直线上的Riemann边值问题,并在正则型的情况给出了方程的可解条件及方程的显式解,特别讨论了解在结点的性态.In this paper, the singular integral equations with convolution kernel will be set up and discussed in the functions class of exponential order increasing. By using Fourier transform and lemmas given in this paper, this class of equation is transferred into the Riemann boundary value problem in two the parallel lines. The general solution and condition of its solvability for the equation are obtained in the normal type case.

关 键 词：奇异积分方程 RIEMANN边值问题 指数增长的函数类 正则型. 

分 类 号：O175.5[理学—数学]