A Schur-Nevanlinna type algorithm for the truncated matricial Hausdorff moment problem
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.03365
- arXiv:
- arXiv:2005.03365
- Bibcode:
- 2020arXiv200503365F
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 44A60;
- 47A57;
- 30E05