多连通区域内带两个位移的Hilbert边值问题

来源期刊：中南大学学报(自然科学版)1990年第5期

论文作者：吕德

文章页码：544 - 550

关键词：边值问题； 两个位移； 奇异积分方程

Key words：boundary value problems； two shifts； singular integral equation

摘    要：

本文利用带两个Carleman位移的奇异积分方程的Noether理论,讨论有界或无界多连通区域内解析函数的Hilbert边值问题。文中给出了此问题的Noether性条件、指数公式和可解的充分必要条件。

Abstract: In this paper,Hilbert boundary value problems with two shifts for ana-lytic functions in bounded or unbounded multiple connected region is discussedwith the help of Noether′s theory for singular integral equation with twoCarleman′s shifts.This paper also provides Noether′s conditions,the formulaof index,and the necessary and sufficient conditions of solvability for theabove problems as well.