# The Jet of an Interpolant on a Finite Set

### Charles Fefferman

Princeton University, United States### Arie Israel

University of Texas at Austin, USA

## Abstract

We study functions $F∈C_{m}(R_{n})$ having norm less than a given constant $M$, and agreeing with a given function $f$ on a finite set $E$. Let $Γ_{f}(S,M)$ denote the convex set formed by taking the $(m−1)$-jets of all such $F$ at a given finite set $S⊂R_{n}$. We provide an efficient algorithm to compute a convex polyhedron $Γ~_{f}(S,M)$, such that $$ \Gamma_f (S,cM) \subset \tilde{\Gamma}_f (S,M) \subset \Gamma_f (S,CM), $where$c$and$C$dependonlyon$m$and$n$.

## Cite this article

Charles Fefferman, Arie Israel, The Jet of an Interpolant on a Finite Set. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 355–360

DOI 10.4171/RMI/639