On primary decomposition of Hermite projectors

08/26/2022

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by   Jaroslaw Buczynski, et al.

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An ideal projector on the space of polynomials ℂ [𝐱]=ℂ [x_1,… ,x_d] is a projector whose kernel is an ideal in ℂ[ 𝐱]. The question of characterization of ideal projectors that are limits of Lagrange projector was posed by Carl de Boor. In this paper we make a contribution to this problem. Every ideal projector P can be written as a sum of ideal projector ∑ P^(k) such that ∩ P^(k) is a primary decomposition of the ideal P. We show that P is a limit of Lagrange projectors if and only if each P^(k) is. As an application we construct an ideal projector P whose kernel is a symmetric ideal, yet P is not a limit of Lagrange projectors.