Opuscula Math. 36, no. 3 (2016), 409-423
http://dx.doi.org/10.7494/OpMath.2016.36.3.409

 
Opuscula Mathematica

Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures

Marcin J. Zygmunt

Abstract. The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is stated the condition on the coefficients of the recurrence formula for which the matrix measure is symmetric.

Keywords: matrix orthogonal polynomials, recurrence formula, matrix of measures, block Jacobi matrices.

Mathematics Subject Classification: 47B36, 15A57, 39B42, 42C05.

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Cite this article as:
Marcin J. Zygmunt, Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures, Opuscula Math. 36, no. 3 (2016), 409-423, http://dx.doi.org/10.7494/OpMath.2016.36.3.409

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