Revista Matemática Iberoamericana

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Volume 28, Issue 1, 2012, pp. 297–304
DOI: 10.4171/RMI/678

Published online: 2012-01-20

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

Charles Fefferman[1] and Fulvio Ricci[2]

(1) Princeton University, United States
(2) Scuola Normale Superiore, Pisa, Italy

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).

Keywords: $C$-infinity extension, linear extension operator, fan-shaped sets

Fefferman Charles, Ricci Fulvio: Some examples of $C^\infty$ extension by linear operators. Rev. Mat. Iberoamericana 28 (2012), 297-304. doi: 10.4171/RMI/678