Integrating completely unisolvent functions
type: Item
instance of: scholarly article
title: Integrating completely unisolvent functions
zbMATH Open document ID: 0892.41001
published in: Journal of Approximation Theory
publication date: 1995-10-09T00:00:00Z
review text: \(f:\mathbb{R}^n\times I\to\mathbb{R}\) is a continuous function and \(\text{INT}(f)\) is the set of all functions \(x\mapsto f(a_1, \dots, a_n,x)\) from \(\mathbb{R}\) to \(\mathbb{R}\). A function \(g\in \text{INT} (f)\) interpolates \(m\) points \((x_i,y_i)\in I\times R\), \(i=1,2, \dots,m\) if \(g(x_i)=y_i\) for all \(i\). The function \(f\) is \(n\)-unisolvent if for any choice of points \((x_i,y_i)\in I\times R\), \(i=1,2, \dots,n\), \(x_1<x_2< \cdots <x_n\), there exists a uniquely determined \(g\in\text{INT}(f)\) that interpolates all \(n\) points. In this paper, the author shows that the integral of a completely \(n\)-unisolvent function defined on an interval is a completely \((n+1)\)-unisolvent function.
reviewed by: T. Thrivikraman
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 26B15
zbMATH DE Number: 803705
zbMATH Keywords: \(n\)-unisolvent function
zbMATH Keywords: Chebyshev systems
author: Burkard Polster
MaRDI profile type: Publication
full work available at URL: jath.1995.1089
OpenAlex ID: W2036487637
DOI: 10.1006/JATH.1995.1089
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description: scientific article; zbMATH DE number 803705