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

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