The structure of linear extension operators for \(C^m\)
type: Item
instance of: scholarly article
title: The structure of linear extension operators for \(C^m\)
zbMATH Open document ID: 1120.41002
DOI: 10.4171/RMI/495
published in: Revista Matemática Iberoamericana
publication date: 2007-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/43595
review text: Let \(C^m(E)\) denote the Banach space of restrictions to \(E,\) where \(E\subset R^n.\) It is known that \(T:C^m(E)\rightarrow C^m(\mathbb{R}^n)\) such that \(Tf=f\) on \(E\) for any \(f\in C^m(E).\) Here the author shows that \(T\) can be taken to have a simple form, but cannot be taken to have an even simpler form.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A45
zbMATH DE Number: 5177714
zbMATH Keywords: extension operators
zbMATH Keywords: Whitney's extension problem
author: Charles Fefferman
MaRDI profile type: Publication
cites work: Differentiable functions defined in closed sets. A problem of Whitney
cites work: Higher-order tangents and Fefferman's paper on Whitney's extension problem
cites work: Q3696071
cites work: Metric spaces with linear extensions preserving Lipschitz condition
cites work: Q4317270
cites work: The Whitney problem of existence of a linear extension operator
cites work: Whitney's extension problem for multivariate \(C^{1,\omega}\)-functions
cites work: Interpolation and extrapolation of smooth functions by linear operators
cites work: A sharp form of Whitney's extension theorem
cites work: Whitney's extension problem for \(C^m\)
cites work: A generalized sharp Whitney theorem for jets
OpenAlex ID: W2015745335
description: scientific article; zbMATH DE number 5177714