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March, 2005 Interpolation and extrapolation of smooth functions by linear operators
Charles Fefferman
Rev. Mat. Iberoamericana 21(1): 313-348 (March, 2005).

Abstract

Let $C^{m , 1} ( \mathbb{R}^n)$ be the space of functions on $\mathbb{R}^n$ whose $m^{\sf th}$ derivatives are Lipschitz 1. For $E \subset \mathbb{R}^n$, let $C^{m , 1} (E)$ be the space of all restrictions to $E$ of functions in $C^{m,1} ( \mathbb{R}^n)$. We show that there exists a bounded linear operator $T: C^{m , 1} (E) \rightarrow C^{m , 1} ( \mathbb{R}^n)$ such that, for any $f \in C^{m , 1} ( E )$, we have $T f = f$ on $E$.

Citation

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Charles Fefferman. "Interpolation and extrapolation of smooth functions by linear operators." Rev. Mat. Iberoamericana 21 (1) 313 - 348, March, 2005.

Information

Published: March, 2005
First available in Project Euclid: 22 April 2005

zbMATH: 1084.58003
MathSciNet: MR2155023

Subjects:
Primary: 49K24 , 52A35

Keywords: linear operators , Whitney extension problem

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

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Vol.21 • No. 1 • March, 2005
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