实轴上具一阶奇性解的特征奇异积分方程

实轴上具一阶奇性解的特征奇异积分方程 Characteristic Singular Integral Equations Having Singularities of Order One on the Real Axis 胡新华 HU Xing-hua 1 2 first-author 钟寿国 ZHONG Shou-guo 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 把实轴上具一阶奇性解的特征奇异积分方程及其相联方程的求解化为实轴上具一阶奇性解的 Rie mann边值问题讨论,对后者在提法、奇点的对待和典则函数的理解方面作了与传统有所不同的处理,对前者通过对解和可解条件的简化及等价性的讨论,得到解和可解条件的简化形式及推广的Noether定理. Characteristic singular integral equation and its adjoin equation are transferred to Riemann boundary value problems in solutions with singularities of order one on the real axis.For the latter,it is dealed with differently such as singularities,canonical function.For the former, their solutions and simplified conditions of solvability and generalized Noether theorem are abtained by a series of discussions and simplifications. 实轴 特征方程 一阶奇性解 推广的Noether定理 reals axis characteristic equation solution with singularity of order one generalized Noether theorem O175.5 国家自然科学基金（19971064）;高等学校博士学科点专项科研基金（98048627）;武汉大学自强基金资助项目 （201990336） 2005-01-01 2021-04-01 1