关于奇偶截断矩阵汉堡矩问题的一种联合解法
On a Simultaneous Approach to the Even and Odd Truncated Matricial Hamburger Moment Problems
摘要：
本文的主要目标是实现在最一般的情况下，偶数和奇数截断矩阵汉堡矩问题的同时处理。在奇情况下，这些结果对于矩阵情形是全新的，而标量情形最近由V.A. Derkach，S. Hassi和H. S. V. de Snoo.在此之前，G. N. Chen和Y.- J. Hu.我们的方法是基于舒尔分析方法。更确切地说，我们使用两个相互关联的版本的舒尔型算法，即一个代数和一个功能理论。代数版本是在以前的一份文件的作者。它是一个算法，适用于有限或无穷序列的复杂矩阵。我们的舒尔型算法的功能理论版本的建设和调查是本文的中心主题。该算法将被应用于Herglotz-Nevanlinna类的全纯矩阵值函数的相关子类。利用最近关于矩阵值Herglotz-Nevanlinna函数的Moore-Penrose逆的全纯性的结果，我们得到了在最一般情况下所考虑的矩量问题的解集的完整描述.
英文摘要：
The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Hamburger moment problems in the most general case. In the odd case, these results are completely new for the matrix case, whereas the scalar version was recently treated by V. A. Derkach, S. Hassi and H. S. V. de Snoo. The even case was studied earlier by G.-N. Chen and Y.-J. Hu. 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 was worked out in a former paper of the authors. It is an algorithm which is applied to finite or infinite sequences of complex matrices. The construction and investigation of the function-theoretic version of our Schur-type algorithm is a central theme of this paper. This algorithm will be applied to relevant subclasses of holomorphic matrix-valued functions of the Herglotz-Nevanlinna class. Using recent results on the holomorphicity of the Moore-Penrose inverse of matrix-valued Herglotz-Nevanlinna functions, we obtain a complete description of the solution set of the moment problem under consideration in the most general situation.
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