Open Access
January, 2011 The Jet of an Interpolant on a Finite Set
Charles Fefferman , Arie Israel
Rev. Mat. Iberoamericana 27(1): 355-360 (January, 2011).


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


Download Citation

Charles Fefferman . Arie Israel . "The Jet of an Interpolant on a Finite Set." Rev. Mat. Iberoamericana 27 (1) 355 - 360, January, 2011.


Published: January, 2011
First available in Project Euclid: 4 February 2011

zbMATH: 1217.49024
MathSciNet: MR834355

Primary: 49K24 , 52A35

Keywords: algorithm , interpolation , jet , Whitney extension theorem

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 1 • January, 2011
Back to Top