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Asymptotic of Cauchy Biorthogonal Polynomials

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Abstract

We consider sequences of biorthogonal polynomials with respect to a Cauchy-type convolution kernel and give the weak and ratio asymptotic of the corresponding sequences of biorthogonal polynomials. The construction is intimately related with a mixed type Hermite–Padé approximation problem whose asymptotic properties is also revealed.

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Acknowledgements

The authors would like to thank Erwin Miña-Díaz for fruitful discussions related with the proof of Theorem 3.9.

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Authors and Affiliations

  1. Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH, 43403, USA

    U. Fidalgo

  2. Department of Mathematics, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911, Leganés, Madrid, Spain

    G. Lopez Lagomasino

  3. Instituto de Matemática y Física, Universidad de Talca, Camino Lircay S/N, Campus Norte, Talca, Chile

    S. Medina Peralta

Authors
  1. U. Fidalgo
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  2. G. Lopez Lagomasino
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  3. S. Medina Peralta
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Correspondence to G. Lopez Lagomasino.

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U. Fidalgo was supported in part by the research grant MTM2015-65888-C4-2-P of Ministerio de Economía, Industria y Competitividad, Spain.

G. López Lagomasino was supported in part by the research grant PGC2018-096504-B-C33 of Ministerio de Ciencia, Innovación y Universidades, Spain.

S. Medina Peralta was supported by Conicyt Fondecyt/Postdoctorado/ Proyecto 3170112.

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Fidalgo, U., Lopez Lagomasino, G. & Medina Peralta, S. Asymptotic of Cauchy Biorthogonal Polynomials. Mediterr. J. Math. 17, 22 (2020). https://doi.org/10.1007/s00009-019-1455-2

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  • DOI: https://doi.org/10.1007/s00009-019-1455-2

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