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 situations. 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 (Fritzsche et al.: Linear Algebra Appl 590:133–209. https://doi.org/10.1016/j.laa.2019.12.027, 2020), 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.

本文的主要目的是在非退化和退化情况下实现截断矩阵Hausdorff矩问题解集的参数化。我们同时处理偶数和奇数情况。我们的方法基于Schur分析方法。更准确地说，我们使用Schur型算法的两个相互关联的版本，即代数算法和函数理论算法。在我们之前的论文（Fritzsche等人：Linear Algebra Appl 590：133–209。https://doi.org/10.1016/j.laa.2019.12.027，2020）中得出的代数版本是一种算法应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。这使我们能够通过Stieltjes变换对所考虑的弯矩问题的解集进行完整描述。此外，我们将详细讨论特殊的解决方案。