超解析函数在不可求长闭曲线上的Riemann边值问题

ON RIEMANN BOUNDARY VALUE PROBLEM FOR HYPERANALYTIC FUNCTION IN IRRECTIFIABLE CLOSED CURVE

本文研究超解析函数在不可求长Jordan闭曲线上的Riemann边值问题,用完全不同于可求长曲线上的Riemann问题的处理方法,证明了问题的可解性结论,得到了问题的一般解的表示式及可解的充分必要条件。

This paper deals with the Riemann boundary value problem for hypera-nalytie function in irrectifiable Jordan closed curve.We proven the existenceand uniqueness theorem of solution for the jump problem and them have est-ablished an explicit form of the general solutions of the homogeneous and in-homogeneous Riemann problems,but also found necessary and sufficient condi-tions for the solvability of inhomogeneous Riemann problem.