JournalsrmiVol. 27, No. 1pp. 355–360

The Jet of an Interpolant on a Finite Set

  • Charles Fefferman

    Princeton University, United States
  • Arie Israel

    University of Texas at Austin, USA
The Jet of an Interpolant on a Finite Set cover
Download PDF

Abstract

We study functions FCm(Rn)F \in C^m (\mathbb{R}^n) having norm less than a given constant MM, and agreeing with a given function ff on a finite set EE. Let Γf(S,M)\Gamma_f (S,M) denote the convex set formed by taking the (m1)(m-1)-jets of all such FF at a given finite set SRnS \subset \mathbb{R}^n. We provide an efficient algorithm to compute a convex polyhedron Γ~f(S,M)\tilde{\Gamma}_f (S,M), such that $$ \Gamma_f (S,cM) \subset \tilde{\Gamma}_f (S,M) \subset \Gamma_f (S,CM), wherewherecandandCdependonlyondepend only onmandandn$.

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