Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight

被引：3

作者：

Conway, Thomas Oliver ^{[1
]}

Deift, Percy ^{[1
]}

机构：

[1] New York Univ, Courant Inst Math Sci, Dept Math, 251 Mercer Str, New York, NY 10012 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

orthogonal polynomials; Riemann-Hilbert problems; recurrence coefficients; steepest descent method; CURVES;

D O I：

10.3842/SIGMA.2018.056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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), 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.

引用

页数：66

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