Generalized semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918112892289024 |
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| author | Branquinho, Amílcar Foulquié-Moreno, Ana Rampazzi, Karina |
| author_facet | Branquinho, Amílcar Foulquié-Moreno, Ana Rampazzi, Karina |
| contents | In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We deduce properties for the recurrence relation coefficients from differential properties of the weight. We take the so called generalized modified Jacobi and Bessel weights as a case study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective Branquinho, Amílcar Foulquié-Moreno, Ana Rampazzi, Karina Classical Analysis and ODEs 42C05 and 33C45 and 33C47 and 47A56 and 47A75 In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We deduce properties for the recurrence relation coefficients from differential properties of the weight. We take the so called generalized modified Jacobi and Bessel weights as a case study. |
| title | Generalized semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective |
| topic | Classical Analysis and ODEs 42C05 and 33C45 and 33C47 and 47A56 and 47A75 |
| url | https://arxiv.org/abs/2406.07290 |