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.
All Science Journal Classification (ASJC) codes
- Extension operators
- Whitney's extension problem