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What is beyond Szegö's theory of orthogonal polynomials?

  • Attila Máté
  • Paul Nevai
  • Vilmos Totik
Orthogonal Polynomials
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

Consider a system {φn} of polynomials orthonormal on the unit circle with respect to the measure dµ with μ′ > 0 almost everywhere. Then
$$\mathop {\lim }\limits_{n \to \infty } \int_{ - \pi }^\pi {\left| {\left| {\phi _n \left( {e^{i\theta } } \right)} \right|\sqrt {\mu '\left( \theta \right)} - 1} \right|^2 } d\theta = 0.$$
.

This result enables one to extend many results of Szegö's theory to the case μ′ > 0.

Keywords

Unit Circle Orthogonal Polynomial Toeplitz Matrix Toeplitz Matrice Orthonormal Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

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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