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−))d 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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | 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 |
| Цитувати: | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function. Percy Deift and Mateusz Piorkowski. SIGMA 20 (2024), 004, 48 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619749587877888 |
|---|---|
| author | Deift, Percy Piorkowski, Mateusz |
| author_facet | Deift, Percy Piorkowski, Mateusz |
| citation_txt | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function. Percy Deift and Mateusz Piorkowski. SIGMA 20 (2024), 004, 48 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure log(2/(1−))d 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 = +1.
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| first_indexed | 2026-03-14T11:55:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212119 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T11:55:48Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Deift, Percy Piorkowski, Mateusz 2026-01-28T14:00:26Z 2024 Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function. Percy Deift and Mateusz Piorkowski. SIGMA 20 (2024), 004, 48 pages 1815-0659 2020 Mathematics Subject Classification: 42C05; 34M50; 45E05; 45M05 arXiv:2307.09277 https://nasplib.isofts.kiev.ua/handle/123456789/212119 https://doi.org/10.3842/SIGMA.2024.004 We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure log(2/(1−))d 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 = +1. The work of P.D. was supported in part by a Silver Grant from NYU. The work of M.P. was supported by the Methusalem grant METH/21/03– long-term structural funding of the Flemish Government and the National Science Foundation under Grant No.1440140. The authors also gratefully acknowledge the support of MSRI (now the Simons Laufer Mathematical Sciences Institute), where the work in this paper was begun when the authors attended a semester program in Fall 2021. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function Article published earlier |
| spellingShingle | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function Deift, Percy Piorkowski, Mateusz |
| title | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function |
| title_full | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function |
| title_fullStr | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function |
| title_full_unstemmed | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function |
| title_short | Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function |
| title_sort | recurrence coefficients for orthogonal polynomials with a logarithmic weight function |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212119 |
| work_keys_str_mv | AT deiftpercy recurrencecoefficientsfororthogonalpolynomialswithalogarithmicweightfunction AT piorkowskimateusz recurrencecoefficientsfororthogonalpolynomialswithalogarithmicweightfunction |