Extension of smooth functions in infinite dimensions, I:
unions of convex sets
Studia Mathematica, Tome 146 (2001) no. 3, pp. 201-226
Cet article a éte moissonné depuis 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 $E$.
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
Affiliations des auteurs :
C. J. Atkin 1
@article{10_4064_sm146_3_1,
author = {C. J. Atkin},
title = {Extension of smooth functions in infinite dimensions, {I:
} unions of convex sets},
journal = {Studia Mathematica},
pages = {201--226},
year = {2001},
volume = {146},
number = {3},
doi = {10.4064/sm146-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm146-3-1/}
}
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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