多连通区域上一类带开方的Riemann边值问题

On Solution of a Kind of Riemann Boundary Value Problem With Squal Roots Under Jumping Curve

关键词:  Riemann边值问题  指标  多连通区域

Key words:  Riemann boundary value problem  index order at infinity  multiply connected region

摘要:

在由L分割的复平面是L围成的区域S⁺和由l+1个连通分支S_i^-(i=0,1,2,…,l)组成的开集S^-情形下,求出边值问题√ψ⁺(t)=G(t)√ψ^-(t)+g(t)的一般解为ψ(z)=∏(z)X(z)²(1/2πi∫_L(g(t)dt)/(X⁺(t)√∏(t)(t-z))+P_λ(z))².

Abstract:

In this paper, The general solution of analytic functions boundary value problem √ψ⁺ (t)=G (t)√ψ^- (t)+g (t) is discussed when the complex plane is divided into a region S⁺ and an open set S^- by many smooth closed contours and φ^- (z) has a finite order a z=∞, the general solution:ψ (z)=∏ (z) X (z)² (1/2πi∫_L (g (t) dt)/ (X⁺ (t)√∏ (t) (t-z))+P_λ (z))² of analytic functions boundary value problem √ψ⁺ (t)=G (t)√ψ^- (t)+g (t) is given.