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<p>We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From&#xa0;a&#xa0;Riemann–Hilbert problem we derive first and second order differential relations for the matrix orthogonal polynomials and functions of second kind. It is shown that the corresponding matrix recurrence coefficients satisfy a non-Abelian extension of a family of discrete Painlevé d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type.</p>

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Matrix Bessel biorthogonal polynomials: a Riemann–Hilbert approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月17日

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  • Amílcar Branquinho,
  • Ana Foulquié-Moreno,
  • Assil Fradi,
  • Manuel Mañas

摘要

We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann–Hilbert problem we derive first and second order differential relations for the matrix orthogonal polynomials and functions of second kind. It is shown that the corresponding matrix recurrence coefficients satisfy a non-Abelian extension of a family of discrete Painlevé d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type.