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arXiv · 1908.05115

Schur analysis of matricial Hausdorff moment sequences

Bernd Fritzsche·Bernd Kirstein·Conrad Mädler
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Abstract

We develop the algebraic instance of an algorithmic approach to the matricial Hausdorff moment problem on a compact interval $[\alpha,\beta]$ of the real axis. Our considerations are along the lines of the classical Schur algorithm and the treatment of the Hamburger moment problem on the real axis by Nevanlinna. More precisely, a transformation of matrix sequences is constructed, which transforms Hausdorff moment sequences into Hausdorff moment sequences reduced by 1 in length. It is shown that this transformation corresponds essentially to the left shift of the associated sequences of canonical moments. As an application, we show that a matricial version of the arcsine distribution can be used to characterize a certain centrality property of non-negative Hermitian measures on $[\alpha,\beta]$.

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Bernd Fritzsche, Bernd Kirstein, Conrad Mädler. 2019-08-14. Schur analysis of matricial Hausdorff moment sequences. https://arxiv.org/abs/1908.05115

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