Constructive Approximation

, Volume 1, Issue 1, pp 63–69

Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle

  • Attila Máté
  • Paul Nevai
  • Vilmos Totik

DOI: 10.1007/BF01890022

Cite this article as:
Máté, A., Nevai, P. & Totik, V. Constr. Approx (1985) 1: 63. doi:10.1007/BF01890022


Consider a system {φn} of polynomials orthonormal on the unit circle with respect to a measure, withμ′>0 almost everywhere. Denoting bykn the leading coefficient ofφn, a simple new proof is given for E. A. Rakhmanov's important result that limn→∞,kn/kn+1=1; this result plays a crucial role in extending Szegö's theory about polynomials orthogonal with respect to measures with logμ′∈L1 to a wider class of orthogonal polynomials.

AMS classification


Key words and phrases

Orthogonal polynomials Szegö's Theory 

Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • Attila Máté
    • 1
  • Paul Nevai
    • 2
  • Vilmos Totik
    • 3
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA
  3. 3.Bolyai InstituteUniversity of SzegedSzegedHungary

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