实轴上一类二阶矩阵函数的Wiener-Hopf分解及其应用

Wiener-Hopf factorization of a class of matrix functions with order two on the real axis and application

研究了实轴上一类二阶矩阵函数的Wiener-Hopf分解问题,运用黎曼边值问题求解方法构造出了此类矩阵函数的显式分解。作为应用,在合适的条件下研究了实轴上一类带反向平移的黎曼边值问题,通过转化法将其等价变形为矩阵边值问题。

In this paper,Wiener-Hopf factorization of a class of matrix functions with order two on the real axis is considered,by means of solving Riemann boundary value problems,the factor of the matrix function is constructed explicitly. As an application,a class of Riemann boundary value problem with backward shift on the line is discussed under appropriate assumption,and then reduced to the equivalent matrix Riemann boundary value problem by using transformation method,solvability condition and general solution to the original problem are obtained.