Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909512544288768 |
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| author | Branquinho, Amílcar Foulquié-Moreno, Ana Fradi, Assil Mañas, Manuel |
| author_facet | Branquinho, Amílcar Foulquié-Moreno, Ana Fradi, Assil Mañas, Manuel |
| contents | 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 extensions of a family of discrete Painlevé d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach Branquinho, Amílcar Foulquié-Moreno, Ana Fradi, Assil Mañas, Manuel Classical Analysis and ODEs 33C45, 33C47, 42C05, 47A56 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 extensions of a family of discrete Painlevé d-PIV equations. We present some nontrivial examples of matrix orthogonal polynomials of Bessel type. |
| title | Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach |
| topic | Classical Analysis and ODEs 33C45, 33C47, 42C05, 47A56 |
| url | https://arxiv.org/abs/2502.19326 |