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

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Abstract

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.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Russia. e-mail

    A. Aptekarev

  2. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Vigo, Orense, Spain. e-mail

    E. Berriochoa

  3. Departamento de Matemática Aplicada, ETS Ingenieros Industriales, Universidad de Vigo, 36280, Vigo, Spain. e-mail

    A. Cachafeiro

Authors
  1. A. Aptekarev
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  2. E. Berriochoa
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  3. A. Cachafeiro
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Aptekarev, A., Berriochoa, E. & Cachafeiro, A. On a Characterization of Integrability for the Reciprocal Weight of Orthogonal Polynomials on the Circle. Acta Applicandae Mathematicae 61, 81–86 (2000). https://doi.org/10.1023/A:1006492307508

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  • DOI: https://doi.org/10.1023/A:1006492307508

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