具有Hilbert核和周期系数的卷积型奇异积分方程  

Singular Integral Equation of Convolution Type with Hilbert Kernel and Periodical Coefficients

作　　者：李平润[1,2] 

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

出　　处：《应用数学学报》2014年第6期1025-1033,共9页Acta Mathematicae Applicatae Sinica

基　　金：曲阜师范大学校青年基金(XJ201218)资助项目

摘　　要：在函数类L_2[-π,π]中研究了一类含Hilbert核和周期系数的卷积型奇异积分方程,通过本文给出的引理和离散的Laurent变换,把此类奇异积分方程转化为序列方程组或离散跃度问题并对本文提出的离散跃度问题进行了求解与讨论,在L_2[-π,π]中,获得了方程的解和可解条件表达式,从而推广了具有Hilbert核的奇异积分方程的有关结果.In this paper, a class of singular integral equation of convolution type with periodicity and Hilbert kernel in class L2[-π, π] will be set up and discussed, by using the discrete Laurent transform and lemma given in this paper, this equation will be turned into discrete jump problems or system of equations, which are solved and discussed in the same time. The general solutions as well as the conditions of solvability are firstly obtained. So we generalized the results for singular integral equations with Hilbert kernels.

关 键 词：卷积型奇异积分方程 周期系数 HILBERT核 离散跃度问题 Laurent变换 

分 类 号：O175.5[理学—数学] O175.8[理学—基础数学]