A characterization of smoothness for Freud weights
type: Item
instance of: scholarly article
title: A characterization of smoothness for Freud weights
zbMATH Open document ID: 0928.41004
DOI: 10.1016/S0377-0427(98)00177-0
published in: Journal of Computational and Applied Mathematics
publication date: 1999-08-22T00:00:00Z
review text: In this paper, the author studies the rate (or degree) of approximation by weighted polynomials \(P_nW\), where \(P_n\) is a polynomial of degree \(\leq n\), and \(W\) is a Freud weight, such as \(\exp(-| x |^\alpha)\), \(\alpha>1\). Building on earlier work on Jackson and Bernstein theorems for weighted moduli of continuity, the author provides a more precise characterization of some specific rates of approximation. The description of the results involves moduli of continuity and also derivatives of polynomials of best approximation.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1326387
zbMATH Keywords: weighted approximation
zbMATH Keywords: \(K\)-functionals
zbMATH Keywords: Freud weight
author: S. B. Damelin
reviewed by: Doron S. Lubinsky
MaRDI profile type: Publication
cites work: Q4486594
cites work: Smoothness theorems for generalized symmetric Pollaczek weights on \((-1,1)\)
cites work: Moduli of smoothness and \(K\)-functionals in \(L_ p\), \(0<p<1\)
cites work: Inverse Theorem for Best Polynomial Approximation in L p , 0 < p < 1
cites work: Jackson and smoothness theorems for Freud weights in \(L_ p (0<p\leq\infty)\)
cites work: Q3817079
cites work: Forward and converse theorems of polynomial approximation for exponential weights on \([-1,1]\). I
cites work: Forward and converse theorems of polynomial approximation for exponential weights on \([-1,1]\). II
cites work: Q4360405
cites work: Weighted approximation with varying weight
description: scientific article; zbMATH DE number 1326387