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arXiv · 1403.3729

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

A. I. Aptekarev·G. López Lagomasino·A. Mártinez-Finkelshtein
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Abstract

We consider multiple orthogonal polynomials with respect to Nikishin systems generated by two measures $(\sigma_1, \sigma_2)$ with unbounded supports ($\mbox{supp} \, \sigma_1 \subseteq \mathbb{R}_+$, $\mbox{supp} \, \sigma_2 \subseteq \,\mathbb{R}_-$) and $\sigma_2$ is 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.

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A. I. Aptekarev, G. López Lagomasino, A. Mártinez-Finkelshtein. 2014-03-15. On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials. https://arxiv.org/abs/1403.3729

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