Asymptotics of matrix orthogonal polynomials on the real line
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917421329154048 |
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| author | Deaño, Alfredo Román, Pablo |
| author_facet | Deaño, Alfredo Román, Pablo |
| contents | In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well as asymptotic behavior of recurrence coefficients and norms. The main tools are the Riemann-Hilbert formulation and the Deift-Zhou method of steepest descent, adapted to the matrix case. A central role is played by the matrix Szegő function, an object that has independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of matrix orthogonal polynomials on the real line Deaño, Alfredo Román, Pablo Classical Analysis and ODEs 33C45, 34M50, 30E15, 41A60 In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well as asymptotic behavior of recurrence coefficients and norms. The main tools are the Riemann-Hilbert formulation and the Deift-Zhou method of steepest descent, adapted to the matrix case. A central role is played by the matrix Szegő function, an object that has independent interest. |
| title | Asymptotics of matrix orthogonal polynomials on the real line |
| topic | Classical Analysis and ODEs 33C45, 34M50, 30E15, 41A60 |
| url | https://arxiv.org/abs/2508.04908 |