Various characterisations of extended Chebyshev spaces via blossoms
type: Item
instance of: scholarly article
title: Various characterisations of extended Chebyshev spaces via blossoms
zbMATH Open document ID: 1064.41021
author: Marie-Laurence Mazure
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2005-02-22T00:00:00Z
review text: Let \({\mathcal U}\) be an \(n\)-dimensional space of \({C^{n-1}}\) functions \({(n\geq 1)}\) defined on an interval \(I\). Let \({\mathcal E}\) be the space obtained by integration, namely \[ {\mathcal E}:=\{U\in C^{n}(I) \mid U'\in {\mathcal U}\}. \] The author shows that \({\mathcal U}\) is an extended Chebyshev space if and only if \({\mathcal E}\) possesses some properties given in terms of spaces with nonvanishing Wronskians, Bernstein-like bases, B-spline-like bases, blossoms. The sketch of the proof is given.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 2136424
zbMATH Keywords: extended Chebyshev space
zbMATH Keywords: blossom
zbMATH Keywords: Bernstein-like basis
zbMATH Keywords: B-spline basis
MaRDI profile type: Publication
full work available at URL: j.crma.2004.09.031
OpenAlex ID: W1999290897
cites work: Q4381524
cites work: Q5534404
cites work: B-spline bases and osculating flats: One result of H.-P. Seidel revisited
cites work: Blossoming beyond extended Chebyshev spaces
cites work: Blossoming: A geometrical approach
cites work: Blossoms and optimal bases
cites work: Chebyshev spaces and Bernstein bases
cites work: Q4381526
cites work: The geometry of Tchebycheffian splines
cites work: Q3895980
DOI: 10.1016/J.CRMA.2004.09.031
Recommended article: Blossoming beyond extended Chebyshev spaces
Recommended article: Chebyshev spaces with polynomial blossoms
Recommended article: Blossoms of generalized derivatives in Chebyshev spaces
Recommended article: Ready-to-Blossom Bases in Chebyshev Spaces
Recommended article: A characterization of Chebyshev spaces
Recommended article: The fundamental blossoming inequality in Chebyshev spaces. I: Applications to Schur functions
Recommended article: Some new Chebyshev spaces
Recommended article: Extended Chebyshev piecewise spaces characterised via weight functions
Recommended article: Characterisations of Chebyshev sets in \(c_{0}\)
Recommended article: Extended Chebyshev spaces in rationality
description: scientific article; zbMATH DE number 2136424