Clifford分析中无界域上正则函数带Haseman位移的边值问题

The Boundary Value Problem with Haseman Shift for Regular Functions on Unbounded Domains in Clifford Analysis

该文在引入修正的Cauchy核的基础上,讨论了Clifford分析中无界域上正则函数带Haseman位移的边值问题.首先给出了无界域上Cauchy型积分的Plemelj公式,再利用积分方程方法和压缩不动点定理证明了问题解的存在唯一性.

On the basis of the introduction of the modified Cauchy kernel, this paper deals with the boundary value problem with Haseman shift for regular functions on unbounded domains： a（t）φ^＋（t）＋b（t）φ^-（d（t））＋c（t）φ^-（t）=g（t）. Firstly, the authors give the Plemelj formula functions on unbounded domains. Then, by the integral equation method and the fixed-point theorem, the authors prove the existence and uniqueness of the solution for the problem.