A note on the multivariate symmetric Hermite Interpolant

TL;DR

This paper extends the concept of Hermite interpolation to multivariate symmetric polynomials, generalizing Lagrange interpolation to handle root coalescence, building on prior work on symmetric Hermite bases.

Contribution

It introduces a generalized multivariate symmetric Hermite interpolant that accounts for root coalescence, expanding the theoretical framework of symmetric polynomial interpolation.

Findings

Defines multivariate symmetric Hermite interpolant

Extends Lagrange interpolation to root coalescence cases

Builds on previous symmetric Hermite basis results

Abstract

In this note we explicit the notion of Hermite interpolant of a multivariate symmetric polynomial, generalizing the notion of Lagrange interpolant to the case when there are roots coalescence, an extension of the results on the symmetric Hermite interpolation basis by M.-F. Roy and A. Szpirglas.