Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight

作者：Conway Thomas Oliver^*; Deift Percy

来源：Symmetry Integrability and Geometry-Methods and Applications, 2018, 14: 056.

DOI：10.3842/SIGMA.2018.056

• orthogonal polynomials
• Riemann-Hilbert problems
• recurrence coefficients
• steepest descent method

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.

• 出版日期2018