Results in Mathematics

, Volume 36, Issue 3, pp 281–296

Analytic Extension of Smooth Functions

Research article

DOI: 10.1007/BF03322117

Cite this article as:
Langenbruch, M. Results. Math. (1999) 36: 281. doi:10.1007/BF03322117

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 ∈0n. For bounded ultradifferentiable functions ƒ we can obtain \({\widetilde f}\)by means of a continuous linear operator.

Mathematics Subject Classification: Primary

26E05 26E10 46E10 

Keywords

Whitney jets analytic extension ultradifferentiable functions boundary values 

Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OldenburgOldenburgGermany

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