On Primary Decomposition of Hermite Projectors

An ideal projector on the space of polynomials C[x]=C[x1, horizontal ellipsis ,xd] is a projector whose kernel is an ideal in C[x]. Every ideal projector P can be written as a sum of ideal projectors P(k) such that the intersection of their kernels kerP(k) is a primary decomposition of the ideal kerP. In this paper, 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.