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Complex Analysis and Operator Theory

, Volume 13, Issue 1, pp 1–44 | Cite as

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

  • A. E. Choque Rivero
  • C. MädlerEmail author
Article

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.

Keywords

Resolvent matrix Orthogonal matrix polynomials Dyukarev–Stieltjes parameters Schur transformed sequences 

Mathematics Subject Classification

Primary 30E05 42C05 47A56 Secondary 30B70 

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Notes

Acknowledgements

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

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Instituto de Física y MatemáticasUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico
  2. 2.Mathematisches InstitutUniversität LeipzigLeipzigGermany

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