Acta Applicandae Mathematica

, Volume 61, Issue 1–3, pp 81–86 | Cite as

On a Characterization of Integrability for the Reciprocal Weight of Orthogonal Polynomials on the Circle

  • A. Aptekarev
  • E. Berriochoa
  • A. Cachafeiro


We prove a necessary and sufficient condition for integrability of the reciprocal weight function of orthogonal polynomials. The condition is given in terms of the asymptotic behaviour of the norm of extremal polynomials with prescribed coefficients.

orthogonal polynomials extremal problems Szegő"s theory 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • A. Aptekarev
    • 1
  • E. Berriochoa
    • 2
  • A. Cachafeiro
    • 3
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesRussia. e-mail
  2. 2.Departamento de Matemática Aplicada, Facultad de CienciasUniversidad de VigoOrenseSpain. e-mail
  3. 3.Departamento de Matemática Aplicada, ETS Ingenieros IndustrialesUniversidad de VigoVigoSpain. e-mail

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