Communications in Mathematical Analysis

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

Abdon E. Choque Rivero

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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).

Article information

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

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919757

Mathematical Reviews number (MathSciNet)
MR3292961

Zentralblatt MATH identifier
1297.15035

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 Even Number of Moments. Commun. Math. Anal. 17 (2014), no. 2, 82--97. https://projecteuclid.org/euclid.cma/1418919757


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