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arXiv · 2404.07566

Nevai's condition for measures with unbounded supports

Grzegorz Świderski
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Abstract

We study Nevai's condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai's condition locally uniformly on the support of the measure away from a finite explicit set. This allows us to give applications to relative uniform and weak asymptotics of Christoffel-Darboux kernels on the diagonal and to limit theorems for unconventionally normalized global linear statistics of orthogonal polynomial ensembles.

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BibTeXRIS

Grzegorz Świderski. 2024-04-11. Nevai's condition for measures with unbounded supports. https://doi.org/10.1016/j.jat.2025.106232

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