| 具周期性的含卷积核与余割核混合的积分方程 |
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| 引用本文： | 李平润. 具周期性的含卷积核与余割核混合的积分方程[J]. 系统科学与数学, 2010, 30(8): 1148-1155 |
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| 作者姓名： | 李平润 |
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| 作者单位： | 曲阜师范大学数学科学学院,曲阜,273165 |
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| 基金项目： | 曲阜师范大学科研启动基金 |
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| 摘 要： | 运用所给出的引理及离散的Fourier变换, 在$L_2[-pi, pi]$上讨论了一类具周期性的含卷积核与余割核$csc(tau-theta)$混合的奇异积分方程,把此类方程转化为离散跃度问题, 得到了方程的可解条件和一般解的显式.
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| 关 键 词： | 奇异积分方程 卷积核 余割核 周期性 离散的Fourier变换. |
| 收稿时间： | 2009-10-19 |
| 修稿时间： | 2010-06-21 |
THE SINGULAR INTEGRAL EQUATIONS CONTAINING BOTH COSECANT AND CONVOLUTION KERNEL WITH PERIODICITY |
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| LI Pingrun. THE SINGULAR INTEGRAL EQUATIONS CONTAINING BOTH COSECANT AND CONVOLUTION KERNEL WITH PERIODICITY[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(8): 1148-1155 |
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| Authors: | LI Pingrun |
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| Affiliation: | School of Mathematical Sciences, Qufu Normal University, Qufu 273165 |
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| Abstract: | In this paper, a kind of singular integral equation containing both cosecant and convolution kernel with periodicity in class $L_2[-pi, pi]$ is discussed. The problem is turned into simple discrete equation or jumping problem, by using the theory of discrete Fourier transform. The explicit representation of general solution in class $L_2[-pi, pi]$ as well as the condition of solvability are obtained. |
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| Keywords: | Singular integral equations convolution kernel cosecant kernel periodicity discrete Fourier transform. |
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