C1 extensions of functions and stabilization of Glaeser refinements

Bo'az Klartag, Nahum Zobin

Research output: Contribution to journalArticlepeer-review

Abstract

Given an arbitrary set E ⊂ ℝn, n ≥ 2, and a function f: E →ℝ, consider the problem of extending f to a C1 function defined on the entire ℝn. 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 C1 case. Some related questions are discussed.

Original languageEnglish
Pages (from-to)635-669
Number of pages35
JournalRevista Matematica Iberoamericana
Volume23
Issue number2
DOIs
StatePublished - 2007
Externally publishedYes

Keywords

  • Extension of smooth functions
  • Glaeser refinements
  • Whitney problems

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