Whitney extension operators without loss of derivatives

2013/04/10 by Leonhard Frerick, Frerick, Leonhard, Enrique Jordá +3
Mathematics · #47A57 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A57

paper · pdf · doi:10.48550/arxiv.1304.2928

13 pages

arxiv created 2013/08/20 · arxiv updated 2013/08/21

Abstract

For a compact set, we characterize the existence of a linear extension operator E for the space of Whitney jets without loss of derivatives, that is, E satisfies the best possible continuity estimates: The supremum of all partial derivatives up to order n of E(f) is less or equal than a constant times the n-th Whitney norm of f. The characterization is a surprisingly simple purely geometric condition telling in a way that at all its points, the set is big enough in all directions.

Related

• Mityagin's Extension Problem. Progress Report
• On the extension of Whitney ultrajets of Beurling type
• Computability of a Whitney Extension
• A coordinate-free proof of the finiteness principle for the Whitney extension problem
• Whitney-type extension theorems for jets generated by Sobolev functions