四元数分析中一类带共轭带位移的边值问题

A Class of Boundary Value Problem with Conjugate Value and a Kind of Shift in Quaternion Analysis

研究了四元数分析中正则函数的一类带共轭带位移的边值问题.首先设计积分算子,将边值问题转化为积分方程问题,借助积分方程理论和不动点原理证明了边值问题解的存在性,并给出了解的积分表达式.

A Class function is considered in of boundary value problem with Conjugate Value and a kind of shift for regular quaternion Analysis. First, we give some integral operators and transform the problem into an integral equation problem. Applying Schauder fixed-- point theorem, we prove the existence of solution for the problem, and give the representation of solution.