数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1785-1792.doi: 10.1016/S0252-9602(10)60172-5

• 论文 • 上一篇    下一篇

HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

陈吕萍, 钟同德   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2006-02-25 修回日期:2009-01-04 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    The project was supported by the Natural Science Foundation of Fujian Province of China (S0850029, 2008J0206), Innovation Foundation of Xiamen University (XDKJCX20063019), and the National Science Foundation of China (10771174).

HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

 CHEN Lv-Ping, ZHONG Tong-De   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2006-02-25 Revised:2009-01-04 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    The project was supported by the Natural Science Foundation of Fujian Province of China (S0850029, 2008J0206), Innovation Foundation of Xiamen University (XDKJCX20063019), and the National Science Foundation of China (10771174).

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摘要：

A theory of a class of higher order singular integral under the operator (Lf)(u)=1/u1[u1 ∂f}/ ∂u1 (u)-u1 ∂f/ ∂u1 (u)+f(u)] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.

关键词: complex hypersphere, Cauchy integral, higher order singular integral, Hadamard principal value, permutation formula

Abstract:

A theory of a class of higher order singular integral under the operator (Lf)(u)=1/u1[u1 ∂f}/ ∂u1 (u)-u1 ∂f/ ∂u1 (u)+f(u)] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.

Key words: complex hypersphere, Cauchy integral, higher order singular integral, Hadamard principal value, permutation formula

中图分类号: 

  • 32A25
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