| 一类具一阶奇性核的奇异积分方程 |
| |
| 引用本文： | 王小林. 一类具一阶奇性核的奇异积分方程[J]. 数学学报, 2002, 45(5): 891-898. DOI: cnki:ISSN:0583-1431.0.2002-05-008 |
| |
| 作者姓名： | 王小林 |
| |
| 作者单位： | 武汉大学数学系,湖北,武汉,430072 |
| |
| 基金项目： | 国家自然科学基金资助项目（201980633） |
| |
| 摘 要： | 当(?)是复平面C上的光滑封闭曲线,k（z）是在(?)所围成的有界闭区域上连续.在其内部解析的函数时.借助于奇异积分算子的广义逆.讨论了具一阶奇性核的正则型奇异积分方程: 在H类中的求解问题.作为应用,作者给出了当k（z）是一类有理函数时的具体解法,从而统一并推广了 Cauchy核和Hilbert核奇异积分方程的经典结果.
|
| 关 键 词： | 一阶奇性核 奇异积分方程 广义逆 |
| 文章编号： | 0583-1431(2002)05-0891-08 |
| 修稿时间： | 2000-05-23 |
A Class of Singular Integral Equations with Kernel Having Singularities of Order One |
| |
| Xiao Lin WANG. A Class of Singular Integral Equations with Kernel Having Singularities of Order One[J]. Acta Mathematica Sinica, 2002, 45(5): 891-898. DOI: cnki:ISSN:0583-1431.0.2002-05-008 |
| |
| Authors: | Xiao Lin WANG |
| |
| Affiliation: | Xiao Lin WANG(Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China) (Fax: (027)87640256; E-mail: Colmath@whu.edu.cn) |
| |
| Abstract: | Let (?) be a closed smooth contour in the complex plane, which boundsa finite region D+ and is continuous on D+∪(?). Using the generalized inverse of singular integral operators, we solve the following normal type of singular integral equations with kernel having singularities of order one: Applying the results obtained, we also give the solution of singular integral equations in the case when k(z) is a class of rational functions. The classical results for singular integral equation with Cauchy kernel and Hilbert kernel are thus extended. |
| |
| Keywords: | Kernel having singularities of order one Singular integral equation Generalized inverse |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
|
点击此处可从《数学学报》下载全文 |
|
