SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

doi:10.1016/S0252-9602(10)60106-3

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1093-1099.doi: 10.1016/S0252-9602(10)60106-3

SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

钟寿国

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2007-12-25 修回日期:2008-01-09 出版日期:2010-07-20 发布日期:2010-07-20
基金资助:
Supported by the NNSF of China (10471107) and RFDP of Higher Education of China (20060486001)

SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

ZHONG Shou-Guo

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2007-12-25 Revised:2008-01-09 Online:2010-07-20 Published:2010-07-20
Supported by:
Supported by the NNSF of China (10471107) and RFDP of Higher Education of China (20060486001)

摘要/Abstract

摘要：

We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by
this article contain special cases discussed before.

关键词: Singular integral equation, solution with singularities of higher order, real axis, infinite point, class H*_λ_{1, …, λn, λ∞}

Abstract:

Key words: Singular integral equation, solution with singularities of higher order, real axis, infinite point, class H*_λ_{1, …, λn, λ∞}

中图分类号:

45E05

钟寿国. SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER[J]. 数学物理学报(英文版), 2010, 30(4): 1093-1099.

ZHONG Shou-Guo. SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER[J]. Acta mathematica scientia,Series B, 2010, 30(4): 1093-1099.

参考文献

[1] Lu Jianke. Boundary value problems for analytic functions. Singapore: World Scientific, 1993

[2] Lu Jianke. On integral equations along curve, the solution of which having singularities of order one. J Wuhan Univ (Nat Sci Ed), 1964, (1): 1--13 (in Chinese)

[3] Zhong Shouguo. Generalized Noether therorem for singular integral equations in solutions with singularities of higher order. Chin Ann of Math, 1998, 19A}(3): 361--366 (in Chinese)

[4] Zhong Shouguo, Zhao Xinquan. Characteristic singular integral equations in solutions with singularities of higher order (Part I). J Wuhan Univ (Nat Sci Ed), 1997, 43(5): 553--559 (in Chinese)

[5] Zhong Shouguo, Zhao Xinquan. Characteristic singular integral equations in solutions with singularities of higher order (Part II). J Wuhan Univ (Nat Sci Ed), 1998, 44(1): 5--8 (in Chinese)

[6] Zhong Shouguo. Singular integral equations along an open arc with solutions having singularities of higher order. Acta Mathematica Scientia, 2005, 25B(2): 193--200

[7] Zhong Shouguo. Characteristic singular integral equations with singularity-one solutions//Tao Qian, Kit Ian Kou, Yan Yang. Proceedings of Symposium on Hyper-Complex Analysis. Macau: University of Macau, 2008: 97--107

[8] Zhong Shouguo. Characteristic singular integral equations with solutions having singularities of higher order on the real axis. Wuhan University Journal of Natural Sciences, 2009, 14(4): 299--303

[9] Zhong Shouguo. Singular integral equations on the real axis with solutions having singularities of higher order at infinite-point (to appear)

[10] Lu Jianke. Singular integrals of higher order and their applications to solving singular integral equations. Sci and Tech of Wuhan Univ, 1977, (2): 106--122 (in Chinese)

[11] Zhong Shouguo. Several types of formulas to interchanging order of integration for singular integrals of higher
order on the real axis. J of Math (PRC), 2000, 20(3): 355--358 (in Chinese)

SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

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