The structure of linear extension operators for Cm

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Abstract

For any subset E ⊂ ℝn, Cm (E) denote the Banach space of restrictions to E of functions F ∈ Cm (ℝn). It is known that there exist bounded linear maps T : Cm(E) → Cm (ℝn) such that T f = f on E for any f ∈ Cm(E). We show that T can be taken to have a simple form, but cannot be taken to have an even simpler form.

Original languageEnglish (US)
Pages (from-to)269-280
Number of pages12
JournalRevista Matematica Iberoamericana
Volume23
Issue number1
DOIs
StatePublished - Jan 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Extension operators
  • Whitney's extension problem

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