TY - JOUR

T1 - Asymptotics of polynomials orthogonal with respect to a logarithmic weight

AU - Conway, Thomas Oliver

AU - Deift, Percy

N1 - Funding Information:
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.

PY - 2018/6/12

Y1 - 2018/6/12

N2 - In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight (Formula Presented) 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.

AB - In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight (Formula Presented) 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.

KW - Orthogonal polynomials

KW - Recurrence coefficients

KW - Riemann-Hilbert problems

KW - Steepest descent method

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U2 - 10.3842/SIGMA.2018.056

DO - 10.3842/SIGMA.2018.056

M3 - Article

AN - SCOPUS:85050344342

VL - 14

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 056

ER -