Clifford分析中K超正则函数的Riemann边值问题

Riemann boundary value problem for K-hypemonogenic functions in Clifford analysis

Clifford分析中的函数理论被广泛研究,得到的许多结果推广了经典复分析中解析函数的理论。文中研究了Clifford分析中K超正则函数的Riemann边值问题,得到它的一种表示式和Cauchy积分公式等一些性质,利用转化法和积分方程及不动点原理证明了它的一类Riemann边值问题O解的存在唯一性。

The function theory in Clifford analysis are studied extensively nowadays, and many research results develop the theory of analytic function in complex analysis. In 2005, Qiao Yuying studied boundary value problems of K-hypemonogenic functions. K-hypemonogenic functions in Clifford analysis were studied, and a kind of expression and some properties such as Cauchy formula were obtained. The conversion method and integral equation and the fixed point theorem were used to prove the existence and uniqueness of the solution to boundary value problems for K-hypemonogenic function.