一类非退化广义Q—全纯矩阵值函数

A Class of the Non-degenerate Generalized Q-holomorphic Matrix Value Function

本文研究一类非退化m×m阶复值函数矩阵W(Z),它满足矩阵形式的平面一阶偏微分方程组这里A.B.Q都是m×m阶复值函数矩阵,W(z)是未知的,在Q(z)可自交换、Holder连续且特征值的模不等于1的条件下,W(z)称为广义Q-全纯矩阵值函数。本文建立了非退化广义Q-纯矩阵值函数的若干基本定理。

The aim of this paper is to investigate the property for a class of the non-degenerate m × m complex value function matrice W(z), which is soulucion of the first order system of partial differential equation W2 = Q(z)W2 + A W + BWin the complex plane, where A(z),B(z),Q(z) are m x m complex matrice. The matrix Q(z) satisfies the self-commuting condition, Holder-continuous condition and has no eigenvalues of magnitude one.Solu-tions of such a systems will be call generalized Q-holomorphic.We have established the some fundamental theorems for m × m non -degenerate generalized Q-holomorphic matrix value function.