Geodesic
Local Smoothing of Uniformly Smooth Maps
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 44-52

Voir la notice de l'article provenant de la source Math-Net.Ru

We solve the problem on the uniform approximation of uniformly continuous (smooth) maps by maps having the maximum possible local and uniform smoothness. In particular, we prove that each uniformly continuous map of the Hilbert space $l_2$ into itself can be approximated by locally infinitely differentiable maps having a Lipschitz derivative.
Keywords: approximation, smoothing, local smoothness, uniform smoothness, Lipschitz derivative. 
@article{FAA_2006_40_3_a4,
     author = {I. G. Tsar'kov},
     title = {Local {Smoothing} of {Uniformly} {Smooth} {Maps}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {44--52},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a4/}
}
TY  - JOUR
AU  - I. G. Tsar'kov
TI  - Local Smoothing of Uniformly Smooth Maps
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2006
SP  - 44
EP  - 52
VL  - 40
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a4/
LA  - ru
ID  - FAA_2006_40_3_a4
ER  - 
%0 Journal Article
%A I. G. Tsar'kov
%T Local Smoothing of Uniformly Smooth Maps
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2006
%P 44-52
%V 40
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a4/
%G ru
%F FAA_2006_40_3_a4
I. G. Tsar'kov. Local Smoothing of Uniformly Smooth Maps. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 44-52. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a4/