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Riemann Boundary Value Problems with Reflection on the Real Axis and Related Singular Integral Equations
Differential Equations ( IF 0.6 ) Pub Date : 2021-02-21 , DOI: 10.1134/s0012266121010080
A. A. Karelin , A. A. Tarasenko

Abstract

We prove a theorem on the equivalence of a scalar Riemann boundary value problem with a shift-reflection on the real axis and a matrix Riemann boundary value problem without the shift. A relationship between the boundary value problem in question and a boundary value problem with orientation-preserving shift-rotation on the unit circle is established. The operator identities constructed by the present authors in their preceding papers and permitting one to eliminate the shift-reflection from the integral equation corresponding to the boundary value problem are the main research tool.



中文翻译:

具有实轴反射的Riemann边值问题和相关的奇异积分方程

摘要

我们证明了一个标量Riemann边值问题的等价性,它在实轴上有位移反射,而矩阵Riemann边值问题没有等价。建立了所讨论的边界值问题与在单位圆上保持定向移位的边界值问题之间的关系。主要作者是本作者在前几篇论文中构造的操作者身份,并允许他们从与边值问题相对应的积分方程中消除位移反射。

更新日期:2021-02-22
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