# A general approximation theorem of Whitney type.

RACSAM (2003)

- Volume: 97, Issue: 2, page 287-303
- ISSN: 1578-7303

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topLangenbruch, 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 -

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