A generalized sharp whitney theorem for jets

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Abstract

Suppose that, for each point x in a given subset E ⊂ ℝn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ C m,ω(ℝn) and a finite constant M, such that the m-jet of F at x belongs to f (x) + M σ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F,M, provided each σ(x) satisfies a condition that we call "Whitney ω- convexity".

Original languageEnglish (US)
Pages (from-to)577-688
Number of pages112
JournalRevista Matematica Iberoamericana
Volume21
Issue number2
DOIs
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Extension problems
  • Whitney convexity
  • Whitney ω-convexity

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