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Strong Asymptotic of Cauchy Biorthogonal Polynomials and Orthogonal Polynomials with Varying Measure

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Abstract

We give the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the defining measures are supported on bounded nonintersecting intervals of the real line and satisfy Szegő’s condition. The biorthogonal polynomials are connected with certain mixed type Hermite-Padé polynomials, which verify full orthogonality relations with respect to certain varying measures. Thus, the strong asymptotic of orthogonal polynomials with respect to varying measures plays a key role in the study.

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Authors and Affiliations

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

    L. G. González Ricardo & G. López Lagomasino

Authors
  1. L. G. González Ricardo
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  2. G. López Lagomasino
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Correspondence to G. López Lagomasino.

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Communicated by Arno Kuijlaars.

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The author González Ricardo was supported in part by a research fellowship from Department of Mathematics of Universidad Carlos III de Madrid, Spain.

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

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González Ricardo, L.G., López Lagomasino, G. Strong Asymptotic of Cauchy Biorthogonal Polynomials and Orthogonal Polynomials with Varying Measure. Constr Approx 56, 577–618 (2022). https://doi.org/10.1007/s00365-022-09580-7

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  • DOI: https://doi.org/10.1007/s00365-022-09580-7

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