Orthogonal polynomials for exponential weights x2ρe-2Q(x) on [0,d)

Eli Levin; Doron Lubinsky

doi:10.1016/j.jat.2005.02.006

Orthogonal polynomials for exponential weights x^2ρe^-2Q(x) on [0,d)

Eli Levin, Doron Lubinsky

Mathematics discipline

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

Abstract

Let I = [0, d), where d is finite or infinite. Let W_ρ (x) = x^ρ exp (-Q (x)), where ρ > - 1/2 and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight W_ρ², obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.

Original language	English
Pages (from-to)	199-256
Number of pages	58
Journal	Journal of Approximation Theory
Volume	134
Issue number	2
DOIs	https://doi.org/10.1016/j.jat.2005.02.006
State	Published - Jun 2005

Bibliographical note

Funding Information:
∗ Corresponding author. Fax: +1 404 894 4409. E-mail address: lubins [email protected] (D. Lubinsky). 1This author acknowledges s upport by National Science Foundation Grant DMS 0400446.

Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

Keywords

Exponential weights
Laguerre weights
Orthogonal polynomials

Access to Document

10.1016/j.jat.2005.02.006

Cite this

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abstract = "Let I = [0, d), where d is finite or infinite. Let Wρ (x) = xρ exp (-Q (x)), where ρ > - 1/2 and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight Wρ2, obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.",

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KW - Laguerre weights

KW - Orthogonal polynomials

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