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Asymptotics of Hermite–Padé approximants of the First Type for Discrete Meixner Measures

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Abstract

Asymptotics of Hermite–Padé approximants of the first type for Weil functions of discrete Meixner measure and its derivative is studied. We describe a piecewise-analytic curve in the complex plane which attracts part of the zeros of the Meixner multiple orthogonal polynomials. This curve possesses a symmetry property in the equilibrium problem with an external field for logarithmic potential of vector measures with a constraint. Some connection between the considered Hermite–Padé approximants and the theory of Diophantine approximations is presented.

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Funding

This work was supported by the Russian Science Foundation (grant no. 19-71-30004).

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  1. Moscow State University, Keldysh Institute of Applied Mathematics, 125047, Moscow, Russia

    V. N. Sorokin

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  1. V. N. Sorokin
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Correspondence to V. N. Sorokin.

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(Submitted by A. I. Aptekarev)

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Sorokin, V.N. Asymptotics of Hermite–Padé approximants of the First Type for Discrete Meixner Measures. Lobachevskii J Math 42, 2654–2667 (2021). https://doi.org/10.1134/S1995080221110214

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