Some criteria and properties of Chebyshev systems
type: Item
instance of: scholarly article
title: Some criteria and properties of Chebyshev systems
zbMATH Open document ID: 0855.41020
DOI: 10.1007/BF02106843
author: Ioan Raşa
author: L. G. Labsker
published in: Siberian Mathematical Journal
publication date: 1997-01-22T00:00:00Z
review text: Let \(T^n [a, b]\) be the Chebyshev system of \(n\) functions on \([a, b]\). An isolated zero \(t\in [a, b]\) of a continuous function \(x\) is called nodal if either \(t\in \{a, b\}\) or \(t\in ]a, b[\) and the function \(x\) changes sign upon passage across \(t\), and \(t\) is nonnodal otherwise. Some systems of \(n\) continuous functions whose linear spans contain functions with given nodal and non-nodal zeros are introduced. The relation between the introduced systems and the system \(T^n [a, b]\) are studied. The results depend on the value of \(n\in \mathbb{N}\) essentially.
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 917161
zbMATH Keywords: continuous functions
zbMATH Keywords: Chebyshev system
reviewed by: D. K. Ugulava
MaRDI profile type: Publication
cites work: Q4165721
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description: scientific article; zbMATH DE number 917161