摘要
设 (αi,βi) ,i =1 ,… ,m是实轴R上互不交迭的有限开区间 ,令Em =R \∪ mi=1(αi,βi) .称F(z)是函数类Sl(Em)中的一个函数 ,如果它属于l×l矩阵值Nevanlinna函数类且在 ∪ mi=1(αi,βi)上解析并且是Hermite正定的 .本文给出严格Sl(Em)函数类中双边矩阵函数留数插值问题的可解条件和解的参数化表示 .所用的方法是构造一个具有某种对称性的矩阵值函数 ,使之成为所提问题解的系数矩阵 .
Let (α_i,β_i)(i=1,...,m) be m nonoverlapping intervals on the real axis R, and put E_m=R\∪ m_ i=1 (α_i,β_i). A function F(z) is in class S_l(E_m) if it is in the l×l matrix-valued Nevanlinna class and is holomorphic and Hermitian positive definite in the intervals ∪ m_ i=1 (α_i,β_i). The solvability criterion for the two-sided residue interpolation in the strict class S_l(E_m) for matrix functions is given, and a parametrization description of all solutions for the question is presented. The method is based on the construction of a matrix-valued function with some symmetries, which serves as the coefficient matrix in the set of all solutions to the problem.
基金
国家自然科学基金 (10 2 71113)
安徽省教育厅资助项目
