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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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