| 一类奇异积分和Cauchy型积分关于积分曲线的稳定性 |
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| 引用本文： | 王小林,龚亚方.一类奇异积分和Cauchy型积分关于积分曲线的稳定性[J].数学学报,1999,42(2):343-350. |
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| 作者姓名： | 王小林 龚亚方 |
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| 作者单位： | 武汉大学数学系,武汉,430072 |
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| 摘 要： | 本文讨论了当任意给定的f（τ，t）在某个区域E内属于H类时，奇异积分在封闭或开口光滑曲线E发生光滑扰动时的稳定性，并给出了相应的误差估计．作为应用，我们还讨论了当（t）在E内属于H类时，Cauchy型积分，在封闭光滑曲线E发生光滑扰动时的稳定性及误差估计．
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| 关 键 词： | 奇异积分 Cauchy型积分 光滑扰动曲线 稳定性 |
| 修稿时间： | :1996-12-3 |
On Stability of a Class of Singular Integral and Cauchy Type Integral with Respect to Path of Integration |
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| Wang Xiaolin,Gong Yafang.On Stability of a Class of Singular Integral and Cauchy Type Integral with Respect to Path of Integration[J].Acta Mathematica Sinica,1999,42(2):343-350. |
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| Authors: | Wang Xiaolin Gong Yafang |
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| Institution: | Wang Xiaolin; Gong Yafang;(Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China) |
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| Abstract: | Given f(, t) being Holder continuous with respect to T, t in a region E C.For the Cauchy principal integral operator where C E is a close or open smooth curve, We discuss the stability of I(f) when the smoothperturbation of r occurs, and give the corresponding error estimates. Furthermore,when is a close contour and W E H(E), the stability and error estimate of Cauchytype integral . are also given. |
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| Keywords: | Singular integral Cauchy type integral Smooth perturbation Stability |
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