含余割核奇异积分修改的反演问题

含余割核奇异积分修改的反演问题 Modification of the Inversion Problem for Singular Integrals with Cosecant Kernel 高婧 GAO Jing 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 针对含余割核奇异积分反演问题在指标k<0时一般无解的情况,本文提出并求解了两种修改的反演问题.而后一种修改反演问题的提法与此前类似问题颇不相同.由于运用了推广的留数定理和Bertrand型换序公式使本问题及类似问题解法得以简化. As the inversion problem for singular integrals with cosecant kernel usually has no solution in case of index k<0, we proposed and solved two different new forms of modified inversion problem in this paper. And the second form is unprecedented in similar problems. The solutions based on the generalized residue theorem and Bertrand-Poincare formula of singular integrals, which are greatly simplified, can also be used in similar problems. 余割核 奇异积分反演 推广的留数定理 h类 cosecant kernel inversion of singular integrals the generalized residue theorem class h 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）;武汉大学自强创新基金资助 2002-03-01 2021-04-01 3