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 discipline

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
Pages (from-to)	105804
Number of pages	1
Journal	Journal of Approximation Theory
Volume	281
DOIs	https://doi.org/10.1016/j.jat.2022.105804
State	Published - 1 Sep 2022

Bibliographical note

Funding Information:
Research supported by National Science Foundation, USA grant DMS1800251 .

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Orthogonal polynomials
Pointwise asymptotics

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10.1016/j.jat.2022.105804

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KW - Pointwise asymptotics

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Asymptotics for orthogonal polynomials and separation of their zeros

Abstract

Bibliographical note

Keywords

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