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On a Two-Variable Class of Bernstein–Szegő Measures

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Abstract

The one-variable Bernstein–Szegő theory for orthogonal polynomials on the real line is extended to a class of two-variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.

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Authors and Affiliations

  1. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada, 04120, Almería, Spain

    Antonia M. Delgado

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Jeffrey S. Geronimo & Plamen Iliev

  3. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA

    Yuan Xu

Authors
  1. Antonia M. Delgado
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  2. Jeffrey S. Geronimo
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  3. Plamen Iliev
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  4. Yuan Xu
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Corresponding author

Correspondence to Jeffrey S. Geronimo.

Additional information

Communicated by Vilmos Totik.

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Delgado, A.M., Geronimo, J.S., Iliev, P. et al. On a Two-Variable Class of Bernstein–Szegő Measures. Constr Approx 30, 71–91 (2009). https://doi.org/10.1007/s00365-008-9022-2

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  • DOI: https://doi.org/10.1007/s00365-008-9022-2

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