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July, 2005 A Generalized Sharp Whitney Theorem for Jets
Charles Fefferman
Rev. Mat. Iberoamericana 21(2): 577-688 (July, 2005).

Abstract

Suppose that, for each point $x$ in a given subset $E \subset \mathbb{R}^n$, we are given an $m$-jet $f(x)$ and a convex, symmetric set $\sigma(x)$ of $m$-jets at $x$. We ask whether there exist a function $F \in C^{m , \omega} ( \mathbb{R}^n )$ and a finite constant $M$, such that the $m$-jet of $F$ at $x$ belongs to $f ( x ) + M \sigma ( x )$ for all $x \in E$. We give a necessary and sufficient condition for the existence of such $F , M$, provided each $\sigma(x)$ satisfies a condition that we call ``Whitney $\omega$-convexity''.

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Charles Fefferman. "A Generalized Sharp Whitney Theorem for Jets." Rev. Mat. Iberoamericana 21 (2) 577 - 688, July, 2005.

Information

Published: July, 2005
First available in Project Euclid: 11 August 2005

zbMATH: 1102.58004
MathSciNet: MR2174917

Subjects:
Primary: 49K24 , 52A35

Keywords: extension problems , Whitney $\omega$-convexity , Whitney convexity

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.21 • No. 2 • July, 2005
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