## Communications in Mathematical Analysis

- Commun. Math. Anal.
- Volume 17, Number 2 (2014), 66-81.

### 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).

#### Article information

**Source**

Commun. Math. Anal., Volume 17, Number 2 (2014), 66-81.

**Dates**

First available in Project Euclid: 18 December 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.cma/1418919756

**Mathematical Reviews number (MathSciNet)**

MR3292960

**Zentralblatt MATH identifier**

1320.42016

**Subjects**

Primary: 42C05: Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45] 44A60: Moment problems 30E05: Moment problems, interpolation problems

**Keywords**

Blaschke-Potapov factors Hausdorff matrix moment problem Stieltjes parameters

#### Citation

Choque Rivero, Abdon E. Decompositions of the Blaschke-Potapov Factors of the Truncated Hausdorff Matrix Moment Problem: The Case of an Odd Number of Moments. Commun. Math. Anal. 17 (2014), no. 2, 66--81. https://projecteuclid.org/euclid.cma/1418919756