Decompositions of the Blaschke-Potapov Factors of the Truncated Hausdorff Matrix Moment Problem: The Case of an Odd Number of Moments

Abstract

In "Multiplicative Structure of the Resolvent Matrix for the Truncated Matricial Hausdorff Moment Problem", Operator Theory: Advances and Applications, (2012) by the author, a multiplicative decomposition of resolvent matrix $U^{(2n)}$ for the truncated Hausdorff matrix moment (THMM) problem via Blaschke–Potapov factors $b^{(2 j)}$ was obtained. In this work we show that every such Blaschke-Potapov factor can be represented as a product of block tridiagonal matrices containing Stieltjes matrix parameters (SMP) depending on a or b. This SMP are in turn a generalization of the Yu. Dyukarev’s Stieltjes parameters introduced in “Indeterminacy criteria for the Stieltjes matrix moment problem”, Mathematical Notes (2004).