, Volume 36, Issue 3-4, pp 281-296
Date: 17 Apr 2013

Analytic Extension of Smooth Functions

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Abstract

Let F be a closed proper subset of ℝn and let ℰ* be a class of ultradifferentiable functions. We give a new proof for the following result of Schmets and Valdivia on analytic modification of smooth functions: for every function ƒ ∈ ℰ* (ℝn) there is \({\widetilde f} \in {\cal E}_{*}(\rm R ^{n})\) which is real analytic on ℝnF and such that ∂a ƒ ¦ F = ∂a ƒ ¦ F for any a ∈0 n. For bounded ultradifferentiable functions ƒ we can obtain \({\widetilde f}\) by means of a continuous linear operator.

Dedicated to Professor Dr. H. G. Tillmann on the occasion of his 75th birthday