AI 中文总结
本文针对矩阵Nevanlinna–Pick插值问题，建立了类似经典汉堡矩问题不确定性准则的新准则，该准则基于相关矩阵级数的收敛性表述。
AI 中文摘要
经典汉堡矩问题可视为Nevanlinna函数的插值问题，与之密切相关的是Nevanlinna–Pick插值问题，每个问题要么是确定的（有唯一解），要么是不确定的（有无穷多解）。Hamburger基于涉及第一类和第二类经典多项式的两个级数的收敛性，建立了矩问题不确定性的准则。本文针对矩阵Nevanlinna–Pick插值问题，建立了类似的准则，该准则基于涉及第一类和第二类有理函数的矩阵级数的收敛性来表述。
英文摘要
The classical Hamburger moment problem can be viewed as an interpolation problem for Nevanlinna functions. A closely related problem is the Nevanlinna--Pick interpolation problem. Each of these problems is either determinate, with a unique solution, or indeterminate, with infinitely many solutions. Hamburger established a criterion for the indeterminacy of the moment problem in terms of the convergence of two series involving the classical polynomials of the first and second kind. In this paper, we establish an analogous criterion for the matrix Nevanlinna--Pick interpolation problem. The criterion is formulated in terms of the convergence of matrix series involving the rational functions of the first and second kind.
Comments38 pages
