2020/05/07 by Bernd Fritzsche, Fritzsche, Bernd, Bernd Kirstein +3
Computer Science · Mathematics · #30E05 #44A60 #47A57 #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2005.03365
openalex publication_date 2020/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goal of this paper is to achieve a parametrization of the solution\nset of the truncated matricial Hausdorff moment problem in the non-degenerate\nand degenerate situation. We treat the even and the odd cases simultaneously.\nOur approach is based on Schur analysis methods. More precisely, we use two\ninterrelated versions of Schur-type algorithms, namely an algebraic one and a\nfunction-theoretic one. The algebraic version, worked out in our former paper\narXiv:1908.05115, is an algorithm which is applied to finite or infinite\nsequences of complex matrices. The construction and discussion of the\nfunction-theoretic version is a central theme of this paper. This leads us to a\ncomplete description via Stieltjes transform of the solution set of the moment\nproblem under consideration. Furthermore, we discuss special solutions in\ndetail.\n