A general approximation theorem of Whitney type.

Langenbruch, Michael. "A general approximation theorem of Whitney type.." RACSAM 97.2 (2003): 287-303. <http://eudml.org/doc/40977>.

@article{Langenbruch2003,
abstract = {We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions and ultradistributions.},
author = {Langenbruch, Michael},
journal = {RACSAM},
keywords = {Aproximación; Ultradistribuciones; Sobreyectividad; Espacios de Fréchet; Problemas de valor de frontera; Convolución; Funciones ultradiferenciables; Whitney's approximation theorem; Whitney's extension theorem; ultradifferentiable functions; ultradistributions},
language = {eng},
number = {2},
pages = {287-303},
title = {A general approximation theorem of Whitney type.},
url = {http://eudml.org/doc/40977},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Langenbruch, Michael
TI - A general approximation theorem of Whitney type.
JO - RACSAM
PY - 2003
VL - 97
IS - 2
SP - 287
EP - 303
AB - We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions and ultradistributions.
LA - eng
KW - Aproximación; Ultradistribuciones; Sobreyectividad; Espacios de Fréchet; Problemas de valor de frontera; Convolución; Funciones ultradiferenciables; Whitney's approximation theorem; Whitney's extension theorem; ultradifferentiable functions; ultradistributions
UR - http://eudml.org/doc/40977
ER -