Geodesic
Extension of smooth functions in infinite dimensions, I: unions of convex sets
C. J. Atkin1
1 School of Mathematical and Computing Sciences Victoria University of Wellington P.O. Box 600 Wellington, New Zealand
Studia Mathematica, Tome 146 (2001) no. 3, pp. 201-226

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $f$ be a smooth function defined on a finite union $U$ of open convex sets in a locally convex Lindelöf space $E$. If, for every $x\in U$, the restriction of $f$ to a suitable neighbourhood of $x$ admits a smooth extension to the whole of $E$, then the restriction of $f$ to a union of convex sets that is strictly smaller than $U$ also admits a smooth extension to the whole of $E$.
DOI : 10.4064/sm146-3-1
Keywords: smooth function defined finite union convex sets locally convex lindel space every restriction suitable neighbourhood admits smooth extension whole restriction union convex sets strictly smaller admits smooth extension whole

C. J. Atkin 1

1 School of Mathematical and Computing Sciences Victoria University of Wellington P.O. Box 600 Wellington, New Zealand 
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C. J. Atkin. Extension of smooth functions in infinite dimensions, I:
 unions of convex sets. Studia Mathematica, Tome 146 (2001) no. 3, pp. 201-226. doi: 10.4064/sm146-3-1

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