On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials

A. I. Aptekarev   ; G. López Lagomasino   ; A. Martínez-Finkelshtein

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 3, pp. 389-449

Résumé

This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair $(\sigma_1,\sigma_2)$ of measures\linebreak with unbounded supports ($\operatorname{supp}(\sigma_1) \subseteq \mathbb{R}_+$, $\operatorname{supp}(\sigma_2)\subset \mathbb{R}_-$) and with $\sigma_2$ discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on $\mathbb{R}_+$ and a constraint on $\mathbb{R}_-$ is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials. Bibliography: 56 titles.

Détail

Keywords: orthogonality with respect to a discrete measure, weak asymptotics, vector equilibrium problem, Nikishin systems.
Mots-clés : Hermite–Padé approximants, multiple orthogonal polynomials

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