Exact bounds for orthogonal polynomials associated with exponential weights
type: Item
instance of: scholarly article
title: Exact bounds for orthogonal polynomials associated with exponential weights
zbMATH Open document ID: 0605.42019
DOI: 10.1016/0021-9045(85)90070-X
published in: Journal of Approximation Theory
publication date: 1985-01-01T00:00:00Z
review text: The main result is: \(| x| <C_ mn^{1/m}\) implies \(w(x)p^ 2_ n(x)\leq C'n^{-1/m},\) \(n=0,1,2...\); where \(w(x)=\exp (-x^ m)\) for real x, and an even integer m, \(p_ n(x)\) is the normalized orthogonal polynomial of degree n for the weight function w, and C', \(C_ m\) are certain constants. Specifically, for any C with \(0<C<1\) there exists C' so that the inequality holds for \(C_ m=C(B(1/2,m/2))^{1/m},\) (the Beta function).
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 3977640
zbMATH Keywords: normalized orthogonal polynomial
zbMATH Keywords: weight function
zbMATH Keywords: Beta function
author: Paul Nevai
reviewed by: Charles F. Dunkl
MaRDI profile type: Publication
cites work: Q3328828
cites work: Some results on absolute continuity for unbounded Jacobi matrices
cites work: The Absolute Continuity of Phase Operators
cites work: On weighted $ℒ_{1}$-approximation by polynomials
cites work: On polynomial approximation with the weight 363-1363-1363-1
cites work: Q4092279
cites work: Q4771257
cites work: Nonnegative solutions of a nonlinear recurrence
cites work: Asymptotics for Solutions of Smooth Recurrence Equations
cites work: Asymptotic Expansions of Ratios of Coefficients of Orthogonal Polynomials with Exponential Weights
cites work: Extremal Problems for Polynomials with Exponential Weights
cites work: Q4112361
cites work: Q5186142
cites work: Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$
cites work: Q3764454
cites work: ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE REAL AXIS
description: scientific article; zbMATH DE number 3977640