一类实轴上向量边值问题与矩阵函数分解  

A Class of Vector-Valued Boundary Problem and Factorization of Matrix Functions

作　　者：郭国安[1] 杜金元[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《武汉大学学报（理学版）》2007年第5期509-512,共4页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(10471107);高等学校博士学科点专项科研基金(20060486001)资助项目

摘　　要：通过引进奇异积分算子和矩阵函数分解的概念,研究了实轴上一类向量Riemann边值问题与奇异积分算子、矩阵函数分解之间的关系.在实轴上向量边值问题的系数矩阵满足某种分解条件下,给出了其可解的充要条件和解的封闭形式及与奇异积分算子之间的等价关系,并给出了一类矩阵函数的亚纯分解的显形式.We introduce singular integral operator and notion of factorization of matrix function, study the relations between a class of vector-valued Riemann boundary problem on the real axis, singular integral operator and factorization of matirx function. We obtain the necessary and sufficient conditions for solvabiliy of vector-valued Riemann boundary problem on the real axis and the close form of solution in the case of coefficient matrix of vector-valued Riemann boundary problem satisfying appropriate factorization, furthermore, we also obtain explicit mermorphic factorization form of a class of matrix functions.

关 键 词：Cauchy积分算子 TOEPLITZ算子 典则分解 

分 类 号：O175.5[理学—数学]