A Class of Vector-Valued Boundary Problem and Factorization of Matrix Functions
Jinyuan Du · Journal of Wuhan University · 2007
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.