Certain unbounded Hermite-Fejér interpolatory polynomial operators
type: Item
instance of: scholarly article
title: Certain unbounded Hermite-Fejér interpolatory polynomial operators
zbMATH Open document ID: 0777.41001
DOI: 10.1007/BF00052097
author: S. Singh
published in: Acta Mathematica Hungarica
publication date: 1993-04-01T00:00:00Z
review text: The paper deals with the generalized Hermite-Fejér interpolatory polynomial \(L_{m,n}[f,x]\) given by \(L_{m,n}[f,x_ k]=f(x_ k)\), \(L^{(j)}_{m,n}[f,x_ k]=0\), \(k=1,2,\dots,n\), \(j=1,2,\dots,m-1\), \(f\in C[-1,1]\), where the \(x_ k\), \(k=1,2,\dots,n\) denote the zeroes of the \(n\)-th Chebyshev polynomial \(T_ n\), \(n=1,2,3,\dots\). The result of the paper is to prove that the operator \(L_{m,n}[f]\) is unbounded for all odd numbers \(m\). The case of even numbers \(m\) was already considered in the author's, Hermite-Fejér interpolation prescribing higher order derivatives, in: Progress in Approximation Theory (1991).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 149655
zbMATH Keywords: Hermite-Fejér interpolatory polynomial
zbMATH Keywords: Chebyshev polynomial
reviewed by: Margareta Heilmann
MaRDI profile type: Publication
cites work: Hermite-Fejér interpolations of higher order. I
cites work: Q5534403
full work available at URL: https://doi.org/10.1007/bf00052097
OpenAlex ID: W2332811818
description: scientific article; zbMATH DE number 149655