Asymptotics of polynomials orthogonal with respect to a logarithmic weight

Thomas Oliver Conway, Percy Deift

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number056
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume14
DOIs
StatePublished - Jun 12 2018

Keywords

  • Orthogonal polynomials
  • Recurrence coefficients
  • Riemann-Hilbert problems
  • Steepest descent method

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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