Matricial Canonical Moments and Parametrization of Matricial Hausdorff Moment Sequences
Bernd Fritzsche, Bernd Kirstein, Conrad M\"adler
TL;DR
This paper develops a complete parametrization of matrix-valued moment sequences on compact intervals using symmetric matricial canonical moments, extending scalar theory results to the matrix case.
Contribution
It introduces a symmetric version of matricial canonical moments for parametrizing matrix-valued moment sequences and characterizes their distinguished extensions.
Findings
Provides a complete parametrization of matrix-valued moment sequences.
Generalizes scalar canonical moments to the matrix setting.
Characterizes distinguished extensions of finite moment sequences.
Abstract
In this paper we study moment sequences of matrix-valued measures on compact intervals. A complete parametrization of such sequences is obtained via a symmetric version of matricial canonical moments. Furthermore, distinguished extensions of finite moment sequences are characterized in this framework. The results are applied to the underlying matrix-valued measures, generalizing some results from the scalar theory of canonical moments.
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