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

Commun. Math. Anal.
Volume 17, Number 2 (2014), 82 - 97

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

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Abstract

We obtain multiplicative decompositions of the Blaschke–Potapov factors of the truncated Hausdorff matrix moment (THMM) problem in the case of an even number of moments. Our result develops the multiplicative representation of the resolvent matrix of the THMM problem in the case of even number of moments by I. Serikova in "The multiplicative structure of resolvent matrix of the moment problem on the kompact interval (case of even numbers of moments)", Vestnik Kharkov Univ. Ser. Mat. Prikl. Mat. i Mekh. no. 790 (2007). We show that every such Blaschke-Potapov factor can be represented as a product of tridiagonal block matrices containing Stieltjes matrix parameters (SMP) depending on a and b. These SMP in turn area generalization of the Dyukarev’s Stieltjes parameters introduced in ”Indeterminacy criteria for the Stieltjes matrix moment problem,” Mathematical Notes, Vol. 75 (2004).