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August, 2007 $C^1$ extensions of functions and stabilization of Glaeser refinements
Bo'az Klartag, Nahum Zobin
Rev. Mat. Iberoamericana 23(2): 635-669 (August, 2007).


Given an arbitrary set $E \subset \mathbb R^n$, $n\ge 2$, and a function $f: E \rightarrow \mathbb R$, consider the problem of extending $f$ to a $C^1$ function defined on the entire $\mathbb R^n$. A procedure for determining whether such an extension exists was suggested in 1958 by G. Glaeser. In 2004 C. Fefferman proposed a related procedure for dealing with the much more difficult cases of higher smoothness. The procedures in question require iterated computations of some bundles until the bundles stabilize. How many iterations are needed? We give a sharp estimate for the number of iterations that could be required in the $C^1$ case. Some related questions are discussed.


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Bo'az Klartag. Nahum Zobin. "$C^1$ extensions of functions and stabilization of Glaeser refinements." Rev. Mat. Iberoamericana 23 (2) 635 - 669, August, 2007.


Published: August, 2007
First available in Project Euclid: 26 September 2007

zbMATH: 1140.46010
MathSciNet: MR2371439

Primary: ‎46E15
Secondary: 46B99 , 46E35

Keywords: extension of smooth functions , Glaeser refinements , Whitney problems

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 2 • August, 2007
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