Revista Matemática Iberoamericana

The Jet of an Interpolant on a Finite Set

Charles Fefferman and Arie Israel

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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 $n$.

Article information

Rev. Mat. Iberoamericana, Volume 27, Number 1 (2011), 355-360.

First available in Project Euclid: 4 February 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49K24 52A35: Helly-type theorems and geometric transversal theory

interpolation jet algorithm Whitney extension theorem


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

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