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.