超解析函数的半连续Riemann边值问题

On Semicontinuous Riemann Problems of Hyperanalytic Function in Jordan Closed Curve

本文研究超解析函救在一般的非光滑或不可求长Jordan闭曲线上的半连续Riemann边值问题,其边界联结条件具有第一类间断或幂间断.我们利用Whitney延拓方法和积分算子方法,证明半连续Riemann问题解的存在唯一性定理,得到了解的一般表示式及非齐次问题可解的充分必要条件.

Suppose L is a Jordan closed curve which is rough or irrectifiable, theset E = {zj}j=1,Aj=This paper deals with the semicontinuous Riemann boundary value problems of hyperanalytic function. We have established on expticit form of the general solution of the Riemann problems, but also found necessary and sufficient conditions for the solvability of the above boundary value problems.