Spectral problems for generalized Jacobi matrices
Spectral problems for generalized Jacobi matrices
复制标题
广义雅可比矩阵的谱问题
DOI：
10.1016/j.laa.2003.11.003
复制
发表时间：
2004
影响因子：
1.1
通讯作者：
V. Derkach
中科院分区：
文献类型：
--
作者：
Maxim S. Derevyagin;V. Derkach
介绍了一类新的广义雅可比矩阵。证明了每一个固有实有理函数是唯一有限广义雅可比矩阵的m函数。此外，每一个作为确定不定矩问题解的广义Nevanlinna函数m（·）都是一个唯一的无限广义Jacobi矩阵的m函数。我们使用的方法是基于逐步求解不定矩问题的舒尔过程。研究了相应的Hamburger级数的次对角线Pade逼近序列的收敛性。
A new class of generalized Jacobi matrices is introduced. Every proper real rational function is proved to be the m-function of a unique finite generalized Jacobi matrix. Moreover, every generalized Nevanlinna function m(·) which is a solution of a determinate indefinite moment problem turns out to be the m-function of a unique infinite generalized Jacobi matrix. The method we use is based on the step-by-step Schur process of solving the indefinite moment problem. The convergence of the sequence of subdiagonal Pade approximants for the corresponding Hamburger series is investigated.