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 language | English (US) |
---|---|
Pages (from-to) | 269-280 |
Number of pages | 12 |
Journal | Revista Matematica Iberoamericana |
Volume | 23 |
Issue number | 1 |
DOIs | |
State | Published - 2007 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
Keywords
- Extension operators
- Whitney's extension problem