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arXiv · 2203.14837

Christoffel functions for multiple orthogonal polynomials

Grzegorz Świderski·Walter Van Assche
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Abstract

We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of $\tfrac{1}{n} K_n(x,x)\, d\mu$ is the same as the limit of the normalized zero counting measure of type II multiple orthogonal polynomials. We also study an extension of Nevai's operators to our context.

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Grzegorz Świderski, Walter Van Assche. 2022-03-28. Christoffel functions for multiple orthogonal polynomials. https://doi.org/10.1016/j.jat.2022.105820

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