Orthogonal polynomials for exponential weights x2 ρ e- 2 Q ( x ) on [ 0, d ), II

Eli Levin; Doron Lubinsky

doi:10.1016/j.jat.2005.05.010

Orthogonal polynomials for exponential weights x^{2 ρ} e^{- 2 Q ( x )} on [ 0, d ), II

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 fenced(x) = x^ρ exp fenced(- Q fenced(x)), where ρ > - frac(1, 2) and Q is continuous and increasing on I, with limit ∞ at d. We obtain further bounds on the orthonormal polynomials associated with the weight W_ρ², finer spacing on their zeros, and estimates of their associated fundamental polynomials of Lagrange interpolation. In addition, we obtain weighted Markov and Bernstein inequalities.

Original language	English
Pages (from-to)	107-143
Number of pages	37
Journal	Journal of Approximation Theory
Volume	139
Issue number	1-2
DOIs	https://doi.org/10.1016/j.jat.2005.05.010
State	Published - Mar 2006

Bibliographical note

Funding Information:
∗ Corresponding author. Fax: 404 894 4409. E-mail address: [email protected] (Doron Lubinsky). 1Research of second author supported by NSF grant DMS 0400446.

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abstract = "Let I = [ 0, d ), where d is finite or infinite. Let Wρ fenced(x) = xρ exp fenced(- Q fenced(x)), where ρ > - frac(1, 2) and Q is continuous and increasing on I, with limit ∞ at d. We obtain further bounds on the orthonormal polynomials associated with the weight Wρ2, finer spacing on their zeros, and estimates of their associated fundamental polynomials of Lagrange interpolation. In addition, we obtain weighted Markov and Bernstein inequalities.",

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Orthogonal polynomials for exponential weights x^{2 ρ} e^{- 2 Q ( x )} on [ 0, d ), II

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