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.
Keywords
Resolvent matrix Orthogonal matrix polynomials Dyukarev–Stieltjes parameters Schur transformed sequencesMathematics Subject Classification
Primary 30E05 42C05 47A56 Secondary 30B70Preview
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Acknowledgements
The authors would like to acknowledge the valuable comments and suggestions of the referee.
References
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