TY - JOUR
T1 - Asymptotics of polynomials orthogonal with respect to a logarithmic weight
AU - Conway, Thomas Oliver
AU - Deift, Percy
N1 - Publisher Copyright:
© 2018, Institute of Mathematics. All rights reserved.
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
SN - 1815-0659
VL - 14
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
M1 - 056
ER -