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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209516 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight |
| spellingShingle |
Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight Conway, T.O. Deift, P. |
| title_short |
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_sort |
asymptotics of polynomials orthogonal with respect to a logarithmic weight |
| author |
Conway, T.O. Deift, P. |
| author_facet |
Conway, T.O. Deift, P. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209516 |
| 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. |
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AT conwayto asymptoticsofpolynomialsorthogonalwithrespecttoalogarithmicweight AT deiftp asymptoticsofpolynomialsorthogonalwithrespecttoalogarithmicweight |
| first_indexed |
2025-12-07T18:01:27Z |
| last_indexed |
2025-12-07T18:01:27Z |
| _version_ |
1850886079990726656 |