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The Resolvent Matrix for the Hausdorff Matrix Moment Problem Expressed in Terms of Orthogonal Matrix Polynomials

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Abstract

This paper continues the former joint investigations of the author with Yu. M. Dyukarev, B. Fritzsche and B. Kirstein on the matrix version of the truncated Hausdorff power moment problem on an intervall \([a,b]\) for a given sequence \((s_j)_{j=0}^{2n}\) of complex \(q\times q\) matrices. The main aim is to obtain more information on the resolvent matrix. We show that the canonical \({q\times q}\) blocks of the resolvent matrix are \(q\times q\) matrix polynomials having special orthogonality properties with respect to the original data \((s_j)_{j=0}^{2n}\).

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Acknowledgments

Many thanks to Prof. Bernd Kirstein of Leipzig University for helpful suggestions. The author also wishes to thank Dr. Conrad Mädler of Leipzig University for valuable comments.

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Authors and Affiliations

  1. Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, C.P. 58048 , Morelia, Michoacán, México

    Abdon Eddy Choque Rivero

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  1. Abdon Eddy Choque Rivero
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Correspondence to Abdon Eddy Choque Rivero.

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Communicated by Bernd Kirstein.

This work was completed with the support of CIC–UMSNH, PROMEP Red de CAs and CONACyT Grant 153184, México.

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Choque Rivero, A.E. The Resolvent Matrix for the Hausdorff Matrix Moment Problem Expressed in Terms of Orthogonal Matrix Polynomials. Complex Anal. Oper. Theory 7, 927–944 (2013). https://doi.org/10.1007/s11785-012-0255-5

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  • DOI: https://doi.org/10.1007/s11785-012-0255-5

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