Blossoms of generalized derivatives in Chebyshev spaces
type: Item
instance of: scholarly article
title: Blossoms of generalized derivatives in Chebyshev spaces
zbMATH Open document ID: 1065.65045
author: Marie-Laurence Mazure
published in: Journal of Approximation Theory
publication date: 2005-02-22T00:00:00Z
review text: The aim of this paper is to extend the classical formulas on the blossoms of the derivative of a several variables polynomial function to the Chebyshev framework. In any extended Chebyshev space it is possible to associate appropriate differential operators which, in this setting, play the same role as the ordinary derivatives in the polynomial space, and which are named ``generalized derivatives''. To define the blossoms in the extended Chebyshev space it is necessary to work in projective spaces. The central result of this paper is Theorem 1, which gives an explicit formula for obtaining the blossoms of the generalized derivative in the \(n\)-dimensional extended Chebyshev space. As applications of this formula, the author gives a formula to obtain the so called Chebyshev-Bézier points of a function and also an iterative differentiation formula for blossoms.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 2136995
zbMATH Keywords: extended Chebyshev spaces
zbMATH Keywords: Chebyshev blossoms
zbMATH Keywords: generalized derivatives
zbMATH Keywords: projective spaces
zbMATH Keywords: Chebyshev-Bézier points
zbMATH Keywords: iterative differentiation formula
MaRDI profile type: Publication
full work available at URL: j.jat.2004.06.004
OpenAlex ID: W2022697782
cites work: Q5534404
cites work: Blossoming: A geometrical approach
cites work: Nested sequences of Chebyshev spaces and shape parameters
cites work: Q4381526
cites work: The geometry of Tchebycheffian splines
cites work: Blossoms are polar forms
cites work: Q5551608
DOI: 10.1016/J.JAT.2004.06.004
description: scientific article; zbMATH DE number 2136995