带位移奇异积分方程组的Noether可解性和正则化

The Noether's Solubility and Regularization of these Systems of Singular Integral Equation with Shift

文中研究了一类带有Ｃａｒｌｅｍａｎ位移项的一般形式奇异积分方程组，与之等价的是一个含有四个元素的边值问题．对其特征方程组，得到在某些条件下的Ｎｏｅｔｈｅｒ可解性结果；而对于含弱奇核项的一般形式方程组，则解决了其方程组的正则化问题，从而建立了广义Ｎｏｅｔｈｅｒ可解性定理．

In this paper, one will consider a class of these systems of singular integral equation with Carleman's shift, which are equivalent to a boundary value problem of quaternion numbers. For their eigen-equation systems, one will obtain Noether's solubility under some conditions. For general forms of equation systems with these terms of weak-singularity, one will resolve their regularization and establish the theorem of generalized Noether's solubility.