Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function
We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure log(2/(1−𝑥))d𝑥 on (−1, 1). The asymptotic formula confirms a special case of a conjecture by Magnus and extends earlier results by Conway and one of the authors. The proof relies on th...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212119 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function. Percy Deift and Mateusz Piorkowski. SIGMA 20 (2024), 004, 48 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure log(2/(1−𝑥))d𝑥 on (−1, 1). The asymptotic formula confirms a special case of a conjecture by Magnus and extends earlier results by Conway and one of the authors. The proof relies on the Riemann-Hilbert method. The main difficulty in applying the method to the problem at hand is the lack of an appropriate local parametrix near the logarithmic singularity at 𝑥 = +1.
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| ISSN: | 1815-0659 |