| 含余割核奇异积分修改的反演问题 |
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| 引用本文： | 高婧,钟寿国.含余割核奇异积分修改的反演问题[J].武汉大学学报(理学版),2002,48(3):269-273. |
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| 作者姓名： | 高婧 钟寿国 |
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| 作者单位： | 武汉大学,数学与统计学院,湖北,武汉,430072 |
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| 基金项目： | 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 |
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| 摘 要： | 针对含余害核奇异积分反演问题在指κ＜0时一般无解的情况，本文提出并求解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。
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| 关 键 词： | 余割核 奇异积分 反演问题 留数定理 h类 |
| 文章编号： | 0253-9888(2002)03-0269-05 |
| 修稿时间： | 2001年11月20 |
Modification of the Inversion Problem for Singular Integrals with Cosecant Kernel |
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| GAO Jing,ZHONG Shou-guo.Modification of the Inversion Problem for Singular Integrals with Cosecant Kernel[J].JOurnal of Wuhan University:Natural Science Edition,2002,48(3):269-273. |
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| Authors: | GAO Jing ZHONG Shou-guo |
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| Abstract: | 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. |
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| Keywords: | cosecant kernel inversion of singular integrals the generalized residue theorem class h |
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