The Structure of Linear Extension Operators for $C^m$
Fefferman, Charles
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 269-280 / Harvested from Project Euclid
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For any subset $E \subset \mathbb{R}^n$, let $C^m (E)$ denote the Banach space of restrictions to $E$ of functions $F \in C^m (\mathbb{R}^n)$. It is known that there exist bounded linear maps $T:C^m(E)\longrightarrow C^m(\mathbb{R}^n)$ such that $Tf = f$ on $E$ for any $f \in C^m (E)$. We show that $T$ can be taken to have a simple form, but cannot be taken to have an even simpler form.
Publié le : 2007-04-14
Classification:  extension operators,  Whitney's extension problem,  41A05,  41A45 
@article{1180728894,
     author = {Fefferman, Charles},
     title = {The Structure of Linear Extension Operators for $C^m$},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 269-280},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1180728894}
}

Fefferman, Charles. The Structure of Linear Extension Operators for $C^m$. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  269-280. http://gdmltest.u-ga.fr/item/1180728894/