Extension of smooth functions in infinite dimensions, I: unions of convex sets

C. J. Atkin. "Extension of smooth functions in infinite dimensions, I: unions of convex sets." Studia Mathematica 146.3 (2001): 201-226. <http://eudml.org/doc/284444>.

@article{C2001,
abstract = {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 ∈ 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.},
author = {C. J. Atkin},
journal = {Studia Mathematica},
keywords = {locally convex Lindelöf space; smooth extension},
language = {eng},
number = {3},
pages = {201-226},
title = {Extension of smooth functions in infinite dimensions, I: unions of convex sets},
url = {http://eudml.org/doc/284444},
volume = {146},
year = {2001},
}

TY - JOUR
AU - C. J. Atkin
TI - Extension of smooth functions in infinite dimensions, I: unions of convex sets
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 3
SP - 201
EP - 226
AB - 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 ∈ 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.
LA - eng
KW - locally convex Lindelöf space; smooth extension
UR - http://eudml.org/doc/284444
ER -