论文标题
用于截短的母亲Hausdorff Moment问题的Schur-Nevanlinna型算法
A Schur-Nevanlinna type algorithm for the truncated matricial Hausdorff moment problem
论文作者
论文摘要
本文的主要目的是在非分类和退化情况下实现截短的母系Hausdorff力矩问题的溶液集的参数化。我们同时对待均匀和奇怪的情况。我们的方法基于Schur分析方法。更确切地说，我们使用两个相互关联的Schur型算法的版本，即代数为代数和函数理论。代数版本是在我们以前的论文Arxiv：1908.05115中进行的，是一种算法，可用于复杂矩阵的有限或无限序列。功能理论版本的构建和讨论是本文的中心主题。这使我们通过正在考虑的瞬间问题的解决方案集的解决方案集进行了完整的描述。此外，我们详细讨论了特殊解决方案。
The main goal of this paper is to achieve a parametrization of the solution set of the truncated matricial Hausdorff moment problem in the non-degenerate and degenerate situation. We treat the even and the odd cases simultaneously. Our approach is based on Schur analysis methods. More precisely, we use two interrelated versions of Schur-type algorithms, namely an algebraic one and a function-theoretic one. The algebraic version, worked out in our former paper arXiv:1908.05115, is an algorithm which is applied to finite or infinite sequences of complex matrices. The construction and discussion of the function-theoretic version is a central theme of this paper. This leads us to a complete description via Stieltjes transform of the solution set of the moment problem under consideration. Furthermore, we discuss special solutions in detail.
