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On Resolvent Matrix, Dyukarev–Stieltjes Parameters and Orthogonal Matrix Polynomials via \([0, \infty )\)-Stieltjes Transformed Sequences

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Abstract

By using Schur transformed sequences and Dyukarev–Stieltjes parameters we obtain a new representation of the resolvent matrix corresponding to the truncated matricial Stieltjes moment problem. Explicit relations between orthogonal matrix polynomials and matrix polynomials of the second kind constructed from consecutive Schur transformed sequences are obtained. Additionally, a non-negative Hermitian measure for which the matrix polynomials of the second kind are the orthogonal matrix polynomials is found.

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Acknowledgements

The authors would like to acknowledge the valuable comments and suggestions of the referee.

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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, Mich, Mexico

    A. E. Choque Rivero

  2. Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109, Leipzig, Germany

    C. Mädler

Authors
  1. A. E. Choque Rivero
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  2. C. Mädler
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Correspondence to C. Mädler.

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Communicated by Daniel Aron Alpay.

A. E. Choque Rivero is supported by SNI–CONACYT and CIC–UMSNH, México.

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Choque Rivero, A.E., Mädler, C. On Resolvent Matrix, Dyukarev–Stieltjes Parameters and Orthogonal Matrix Polynomials via \([0, \infty )\)-Stieltjes Transformed Sequences. Complex Anal. Oper. Theory 13, 1–44 (2019). https://doi.org/10.1007/s11785-017-0655-7

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