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柯西型积分和平面上边值问题
引用本文:郑神州,舒连清.柯西型积分和平面上边值问题[J].北方交通大学学报,2010(3):48-53.
作者姓名:郑神州  舒连清
作者单位:[1]北京交通大学理学院,北京100044 [2]台州学院信息工程学院,浙江临海 317000
基金项目:国家自然科学基金资助项目(10671200)
摘    要:综述平面各种边值问题的发展状况:以Cauchy型主值奇异积分为主线,用Plemelj公式求解基本的依跳跃问题,然后从齐次Riemann边值问题的解公式和典则函数得到非齐次Riemann边值问题的解;将Hilbert边值问题化为Riemann边值问题求解.进一步对周期、双周期、群不变的边值、带位移边值及它们相互之间的复合等各种问题,提供转化为典型问题的进展和文献.

关 键 词:柯西型积分  Riemann边值问题  Hilbert边值问题  周期边值问题  带位移边值问题

Integral of Cauchy Type and Various Boundary-Value Problems in Plane
ZHENG Shenzhou,SHU Lianqing.Integral of Cauchy Type and Various Boundary-Value Problems in Plane[J].Journal of Northern Jiaotong University,2010(3):48-53.
Authors:ZHENG Shenzhou  SHU Lianqing
Institution:1.School of Science,Beijing Jiaotong University,Beijing 100044,China;2.School of Information and Technology,Taizhou College,Linhai Zhejiang,317000,China)
Abstract:We provide the theory and development for various boundary-value problems in the plane.By Starting from a integral of Cauchy type and Plemelj formula,we in turn establish these solutions of jump boundary-value problem,homogeneous Riemann's problem and Riemann's problem defined in a planar simple domain.Then we can transform famous Hilbert's problem into Riemann's problem by means of a symmetric expansion w.r.t.the unit circle.Finally,we present the literatures and developments for these boundary value problem of period,double period,invariant Mobius's group and their compostions each other.
Keywords:integral of cauchy type  Riemann's boundary-value problem  Hilbert's problem  periodic problem  boundary-value problem with shift function
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