Opuscula Mathematica
Opuscula Math. 36, no. 3 (2016), 409-423

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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About the authors ▼
Marcin J. Zygmunt
AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
About the article ▼
Communicated by P.A. Cojuhari.
Received: 2015-03-08.
Revised: 2015-11-25.
Accepted: 2015-11-28.
Published online: 2016-02-21.
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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