On one class of Hermite projectors
type: Item
instance of: scholarly article
title: On one class of Hermite projectors
zbMATH Open document ID: 1354.41029
author: Boris Shekhtman
published in: Constructive Approximation
publication date: 2016-10-21T00:00:00Z
review text: The paper under review concerns \textit{ideal projectors}, more precisely, linear projectors \(P: \mathbb C[x_1,\ldots, x_d] \to \mathbb C[x_1,\ldots, x_d]\) such that the kernel of \(P\) is an ideal defining a \(0\)-dimensional algebraic subset of \(\mathbb C^d\). If the ideal is radical, \(P\) is said to be Lagrange, and Hermite if \(P\) is a limit of Lagrange projectors. The author conjectures that an ideal projector such that the kernel defines a \(0\)-dimensional complete intersection is Hermite, and the conjecture is verified in the case that the generators of the ideal have no roots at infinity.
reviewed by: Ragni Piene
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 14B07
zbMATH DE Number: 6642253
zbMATH Keywords: ideal projector
zbMATH Keywords: Lagrange projector
zbMATH Keywords: Hermite projector
zbMATH Keywords: complete intersection
MaRDI profile type: Publication
full work available at URL: s00365-015-9311-5
OpenAlex ID: W1698169260
cites work: On the pointwise limits of bivariate Lagrange projectors
cites work: Q5465277
cites work: Interpolation from spaces spanned by monomials
cites work: On polynomial ideals of finite codimension with applications to box spline theory
cites work: Hilbert schemes of 8 points
cites work: On the Gorenstein locus of some punctual Hilbert schemes
cites work: Q5690494
cites work: Q4209232
cites work: Apolarity and canonical forms for homogeneous polynomials
cites work: Q4293528
cites work: Q5462454
cites work: H-bases for polynomial interpolation and system solving
cites work: On a conjecture of Carl de Boor regarding the limits of Lagrange interpolants
cites work: Q5443994
cites work: On the limits of Lagrange projectors
cites work: Q3560416
DOI: 10.1007/S00365-015-9311-5
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description: scientific article; zbMATH DE number 6642253