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Strong asymptotics for the Pollaczek multiple orthogonal polynomials

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Abstract

The asymptotic properties of multiple orthogonal polynomials with respect to two Pollaczek weights with different parameters are considered. This set of weights is a Nikishin system generated by two measures with unbounded supports; moreover, the second measure is discrete. During the last years, multiple orthogonal polynomials with respect to Nikishin systems of this type have found wide applications in the theory of random matrices. Strong asymptotic formulas for the polynomials under consideration are obtained by means of the matrix Riemann–Hilbert method.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    A. I. Aptekarev

  2. Department of Mathematics, Universidad Carlos III de Madrid, Leganés, Spain

    G. López Lagomasino

  3. Department of Mathematics, University of Almeria, Almeria, Spain

    A. Martínez-Finkelshtein

Authors
  1. A. I. Aptekarev
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  2. G. López Lagomasino
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  3. A. Martínez-Finkelshtein
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Correspondence to A. I. Aptekarev.

Additional information

Original Russian Text © A.I. Aptekarev, G. López Lagomasino, A. Martínez-Finkelshtein, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 393–397.

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Aptekarev, A.I., López Lagomasino, G. & Martínez-Finkelshtein, A. Strong asymptotics for the Pollaczek multiple orthogonal polynomials. Dokl. Math. 92, 709–713 (2015). https://doi.org/10.1134/S1064562415060216

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  • DOI: https://doi.org/10.1134/S1064562415060216

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