Bounds for weighted Lebesgue functions for exponential weights. II
type: Item
instance of: scholarly article
title: Bounds for weighted Lebesgue functions for exponential weights. II
zbMATH Open document ID: 1012.41003
DOI: 10.1023/A:1020854727886
author: D. G. Kubayi
published in: Acta Mathematica Hungarica
publication date: 2003-05-18T00:00:00Z
review text: For sequences of orthogonal polynomials with respect to a weighted inner product, bounds for the weighted Lebesgue functions are provided. Here, the weights are allowed to be exponentials, i.e. \(W(x)=\exp(-Q(x))\) with continuous and convex \(Q\). Thus the Lebesgue function \(\Lambda_n(x)\) is the sum of moduli of the fundamental functions that are divided by the weight function's values at the respective knots, times \(W(x)\). The main theorem gives a short asymptotic expansion of \(\Lambda_n\) for large \(n\). The improvement of this estimate is due to the use of Szabados' idea of adding two extra knots to the sequence.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 05E35
zbMATH DE Number: 1912071
zbMATH Keywords: Lebesgue function
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: exponential weights
reviewed by: Martin D. Buhmann
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1912071