Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight
In this paper, we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight w(x)dx = log(2k/(1 - x))dx on (-1,1), with k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann-Hilbert/steepest-descent m...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209516 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight / T.O. Conway, P. Deift // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862715928984158208 |
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| author | Conway, T.O. Deift, P. |
| author_facet | Conway, T.O. Deift, P. |
| citation_txt | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight / T.O. Conway, P. Deift // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight w(x)dx = log(2k/(1 - x))dx on (-1,1), with k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann-Hilbert/steepest-descent methods, but not in the standard way, as there is no known parametrix for the Riemann-Hilbert problem in a neighborhood of the logarithmic singularity at x = 1.
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| first_indexed | 2025-12-07T18:01:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209516 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:01:27Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Conway, T.O. Deift, P. 2025-11-24T10:11:46Z 2018 Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight / T.O. Conway, P. Deift // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C47; 34E05; 34M50 arXiv: 1711.01590 https://nasplib.isofts.kiev.ua/handle/123456789/209516 https://doi.org/10.3842/SIGMA.2018.056 In this paper, we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight w(x)dx = log(2k/(1 - x))dx on (-1,1), with k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann-Hilbert/steepest-descent methods, but not in the standard way, as there is no known parametrix for the Riemann-Hilbert problem in a neighborhood of the logarithmic singularity at x = 1. The work of the second author was supported in part by DMS Grant # 1300965. The authors gratefully acknowledge the comments and suggestions about the result in this paper by Arno Kuijlaars and Andrei Martinez-Finkelshtein. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight Article published earlier |
| spellingShingle | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight Conway, T.O. Deift, P. |
| title | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight |
| title_full | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight |
| title_fullStr | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight |
| title_full_unstemmed | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight |
| title_short | Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight |
| title_sort | asymptotics of polynomials orthogonal with respect to a logarithmic weight |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209516 |
| work_keys_str_mv | AT conwayto asymptoticsofpolynomialsorthogonalwithrespecttoalogarithmicweight AT deiftp asymptoticsofpolynomialsorthogonalwithrespecttoalogarithmicweight |