特征奇异积分方程的直接解法

特征奇异积分方程的直接解法 Direct Method of Solution for a Class of Characteristic Singular Integral Equations 杜志华 DU Zhi-hua 1 2 first-author 杜金元 DU Jin-yuan 1 2 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics,Wuhan University School of Mathematics and Statistics,Wuhan University 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 通过引进基本特征方程和基本化算子,研究了带解析系数函数和核密度函数的特征奇异积分方程的直接解法,给出其可解的充要条件和解的封闭形式.本文采用的方法,不同于经典的边值问题解法,特征奇异积分方程无须化为等价的边值问题而实现真正意义上的直接求解. We introduce basic characteristic equations and basic transformation operators,study the direct method of solution for a class of characteristic singular integral equations and obtain the necessary and sufficient conditions for solvability of the equations and the close form of solutions.The method in present paper is different from the classical method based on the theory of boundary value problems.Here some results develop and improve the classical ones. 基本特征方程 基本化算子 直接解法 basic characteristic equations basic transformation operators direct method of solution O241.83 国家自然科学基金资助项目（19971064） 2005-05-01 2021-04-01 5