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

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

Keywords

Exponential weights
Laguerre weights
Orthogonal polynomials

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10.1016/j.jat.2005.02.006

Cite this

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

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.",

keywords = "Exponential weights, Laguerre weights, Orthogonal polynomials",

author = "Eli Levin and Doron Lubinsky",

year = "2005",

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doi = "10.1016/j.jat.2005.02.006",

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T1 - Orthogonal polynomials for exponential weights x2ρe-2Q(x) on [0,d)

AU - Levin, Eli

AU - Lubinsky, Doron

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N2 - 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.

AB - 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.

KW - Exponential weights

KW - Laguerre weights

KW - Orthogonal polynomials

UR - https://www.scopus.com/pages/publications/18744383060

U2 - 10.1016/j.jat.2005.02.006

DO - 10.1016/j.jat.2005.02.006

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AN - SCOPUS:18744383060

SN - 0021-9045

VL - 134

SP - 199

EP - 256

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 2

ER -

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

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Keywords

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