Some examples of $C^\infty$ extension by linear operators

Abstract

For two kinds of sets X in \mathbb{R}^n , we prove the existence of linear continuous operators extending C^\infty functions on X to C^\infty functions on \mathbb{R}^n . The sets we consider are: (a) sequences of points in the real line converging to 0 at a polynomial rate, (b) flag-shaped sets in the plane, which are unions of half-lines with slopes as in (a).