Asymptotics for orthogonal polynomials and separation of their zeros

Eli Levin; D. S. Lubinsky

doi:10.1016/j.jat.2022.105804

Asymptotics for orthogonal polynomials and separation of their zeros

Eli Levin
, D. S. Lubinsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let p_n denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials p_n,p_n−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of p_n−1,p_n, and pointwise asymptotics for the orthogonal polynomials.

Original language	English
Article number	105804
Journal	Journal of Approximation Theory
Volume	281-282
DOIs	https://doi.org/10.1016/j.jat.2022.105804
State	Published - 1 Sep 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Orthogonal polynomials
Pointwise asymptotics

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10.1016/j.jat.2022.105804

Cite this

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abstract = "Let pn denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials pn,pn−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of pn−1,pn, and pointwise asymptotics for the orthogonal polynomials.",

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N2 - Let pn denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials pn,pn−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of pn−1,pn, and pointwise asymptotics for the orthogonal polynomials.

AB - Let pn denote the orthonormal polynomials associated with a measure μ with compact support on the real line. In a recent paper, we showed there is a close relationship between the spacing of zeros of successive orthogonal polynomials pn,pn−1, and uniform bounds on the orthogonal polynomials in subintervals of the support. In this paper, we show there is also a relationship between asymptotics for the spacing of zeros of pn−1,pn, and pointwise asymptotics for the orthogonal polynomials.

KW - Orthogonal polynomials

KW - Pointwise asymptotics

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Asymptotics for orthogonal polynomials and separation of their zeros

Abstract

Bibliographical note

Keywords

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