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在指数增长的函数类中的奇异积分方程与 Riemann 边值问题

李平润   

  1. 中国科学技术大学数学科学学院, 合肥   230026;  曲阜师范大学数学科学学院,曲阜  273165
  • 出版日期:2015-01-25 发布日期:2015-04-08

李平润. 在指数增长的函数类中的奇异积分方程与 Riemann 边值问题[J]. 系统科学与数学, 2015, 35(1): 99-109.

LI Pingrun. THE SINGULAR INTEGRAL EQUATIONS IN FUNCTIONS CLASS OF EXPONENTIAL ORDER INCREASING AND RIEMANN BOUNDARY VALUE PROBLEM[J]. Journal of Systems Science and Mathematical Sciences, 2015, 35(1): 99-109.

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

LI Pingrun   

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026; School of Matheatical Sciences, Qufu Normal University, Qufu 273165
  • Online:2015-01-25 Published:2015-04-08

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\ {\rm 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 {\rm 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.

MR(2010)主题分类: 

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[1] 李平润. 一类含卷积核与Cauchy核的奇异积分微分方程的非正则型解法[J]. 系统科学与数学, 2014, 34(3): 352-361.
[2] 李平润. 具周期性的含卷积核与余割核混合的积分方程[J]. 系统科学与数学, 2010, 30(8): 1148-1155.
[3] 范鹰;胡传淦. 含参数的一类积分方程[J]. 系统科学与数学, 2000, 20(1): 65-070.
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