Dyukarev–Stieltjes parameters of the truncated Hausdorff matrix moment problem

We obtain a new multiplicative decomposition of the resolvent matrix of the non-degenerate truncated Hausdorff matrix moment (THMM) problem in the case of odd and even number of moments with the help of Dyukarev–Stieltjes matrix parameters (DSMP). Our result generalizes the Dyukarev representation o...

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Bibliographic Details
Published in:Boletín de la Sociedad Matemática Mexicana 2017-10, Vol.23 (2), p.891-918
Main Author: Choque-Rivero, Abdon E.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Article
Polynomials
Representations
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Summary:We obtain a new multiplicative decomposition of the resolvent matrix of the non-degenerate truncated Hausdorff matrix moment (THMM) problem in the case of odd and even number of moments with the help of Dyukarev–Stieltjes matrix parameters (DSMP). Our result generalizes the Dyukarev representation of the resolvent matrix of the truncated Stieltjes matrix moment problem published in (Math Notes 75(1–2):66–82, 2004 ). In the scalar case, these parameters appear in the celebrated Stieltjes’s ( 1894 ) work Recherches sur les fractions continues and are used to establish the determinateness of the moment problem. We also obtain explicit relations between four families of orthogonal matrix polynomials on [ a ,  b ] together with their matrix polynomials of the second kind and the DSMP of the THMM problem. Additionally, we derive new representations of the Christoffel–Darboux kernel.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-015-0083-5