F-Ⅰ型算子核为退化核的奇异积分方程

F-Ⅰ型算子核为退化核的奇异积分方程 The Singular Integral Equation with F-Ⅰ Operator Kernel Being Degenerate Kernel 沈艳军 SHEN Yan- jun 1 first-author 钟寿国 ZHONG Shou- guo 1 武汉大学数学与计算机科学学院,湖北,武汉,430072 武汉大学数学与计算机科学学院,湖北,武汉,430072 College of Mathematics and Com puter Science,Wuhan University,Wuhan 0 72 College of Mathematics and Com puter Science,Wuhan University,Wuhan 0 72 用 Vekua正则化方法、Fredholm理论及退化核积分方程理论 ,给出 Fredholm第一型核为退化核的奇异积分方程解和可解条件 ,对 F- 型核为一般连续核和弱奇性核的奇异积分方程也有若干结果 . Using the Vekua method of regularization,the theories of Fredholm and integral equation for degenerate kernel,it is given the solutions and conditions of solvability of singular integral equation which F- type operator kernel is degnerate.It has also the some consequence for singular integral equation which F- operator kernel is general continous kernel or singular kernel with weak singularity. F-Ⅰ型算子 退化核 奇异积分方程 可解条件 F- type operator degenerate kernel singular integral equation conditions of solvability 10.14188/j.1671-8836.2000.05.003 O175.5 国家自然科学基金!（ 199710 64 ）;国家教委博士点基金!（ 980 4862 7）;武汉大学自强创新基金资助项目 2000-05-01 2021-04-01 5