超解析函数在可求长开曲线上的Riemann边值问题

ON RIEMANN BOUNDARY VALUE PROBLEM FOR HYPERANALYTIC FUNCTION IN RECTIFIABLE OPEN CURVE

本文研究下列Riemann边值问题:■其中D=■,i,e是生成Douglis代表数的两个元素,W(z)=■(Z)e^k是未知的超复函数(r为某个自然数),L=■2是可求长的有向Jordon开曲线,■/{α_1,α_2},对于具有性质θ(δ)～δ的非光滑可求长开曲线L=■,本文得到了问题(A)的■(L)类和■_0(L)类一般解的表示式及问题可解的充分必要条件,建立了问题(A)的线性无关解的个数及可解条件的个数与问题(A)的指标之间的关系。

In this paper,we studied Riemann boundary value problem for hyperanalyticfunction in rectifiable open curve:DW(z)=0(zC∈\L),W^+(τ)=C(τ)W^-(τ)+g(τ),τ∈\{α_1,α_2},where ■,Douglis algebra is gener-ated by the two elements i and e,W(z)=■W_K(z)~e^k is an unknown hypercompexfunction(r is a certain natural number),L=■ be the rectifiable Jordan opencurve,■=L\{α_1,α_2}.If L has prpoerty of θ(δ)～δ,then the representation ofgeneral solution of the Riemann problem in class ■(L)and ■_0(L),and necessaryand sufficient condition of Riemann probtem that is solvable are obtained.