Lagrange interpolation polynomials in \(E^ p (D)\) with \(1<p< +\infty\)
type: Item
instance of: scholarly article
title: Lagrange interpolation polynomials in \(E^ p (D)\) with \(1<p< +\infty\)
zbMATH Open document ID: 0872.30021
DOI: 10.1007/BF01874607
author: Yanyan Li
published in: Acta Mathematica Hungarica
publication date: 1997-10-20T00:00:00Z
review text: This paper deals with the approximation problem by the Lagrange interpolation polynomials for the complex functions which belong to a generalized Hardy space \(E^p(D)\) with \(1<p<\infty\), where \(D\) is a Jordan domain with boundary \(\Gamma\) which is assumed to be piecewise \(C^2\) smooth with no cusps in the paper. For a function \(f\in E^p(D)\) its norm \(|f|_p\) is defined as the \(L^p\) norm of its non-tangential boundary value on \(\Gamma\). The author constructed appreciate interpolation nodes \(z_{k,n}\), \(k=0,1,\dots, n-1\), \(n\in\mathbb{N}\), and then proved \[ \lim_{n\to\infty}|f-L_{n-1}|_p=0,\qquad \forall f\in E^p(D), \] where \(L_{n-1}(f)\) denotes the \(n-1\)-th Lagrange interpolation polynomial to \(f\) based on the nodes \(z_{k,n}\), \(k=0,1,\dots, n-1\).
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 878086
zbMATH Keywords: Lagrange interpolation
reviewed by: Wang Kunyang
MaRDI profile type: Publication
cites work: On the degree of polynomial approximation in \(E^p(D)\)
cites work: Q3031404
cites work: Polynomial approximation in \(E^ p(D)\) with \(0<p<1\)
cites work: Convergence of interpolants based on the roots of Faber polynomials
cites work: On the theory of approximation of functions on closed sets of the complex plane (with reference to a problem of S. M. Nikol'skii)
cites work: Convergence of complex Lagrange interpolation polynomials on the locus of the interpolation points
cites work: On Faber polynomials and Faber expansions
cites work: Q5618011
description: scientific article; zbMATH DE number 878086