向量值广义 M解析函数的 Riem ann边值问题(英文)

THE RIEMANN BOUNDARY VALUE PROBLEM FOR VECTOR-VALUED GENERALIZED M-ANALYTIC FUNCTIONS

本文研究了椭圆方程组 Lf≡fx+Mfy+EPfy=0的解所定义的取值于 Banach空间的向量值广义 M-解析函数的 Riemann边值问题 ,其中 M是一个 m× m无实特征值的常数矩阵 ,f是 m× q矩阵 ,E是一个常数幂零 m×m矩阵 ,满足 Er=0 ( r 2 ) ,P是一个 m× m的属于 Hα空间的变量矩阵 ,且在某圆外取值为零矩阵 .

This paper studies Riemann boundary value problem for vector valued generalized M analytic function with range in a Banach space which is defined by the solution of the elliptic system Lf≡f x+Mf y+EPf y =0, where M is an m×m constant matrix with no real eigenvalues, f is an m×q matrix, E is a constant nilpotent m×m matrix satisfying E r =0( r \ 2), P is a variable m×m matrix in the space H α . Also, P vanishes outside some disk. Moreover, its stability is discussed