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

作　　者：高婧[1] 钟寿国[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2002年第3期269-273,共5页Journal of Wuhan University:Natural Science Edition

基　　金：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

摘　　要：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.

关 键 词：余割核 奇异积分 反演问题 留数定理 H类 

分 类 号：O175.5[理学—数学]