Analytic Extension of Smooth Functions |
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Authors: | Michael Langenbruch |
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Affiliation: | 1. Department of Mathematics, University of Oldenburg, 26111, Oldenburg, Germany
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Abstract: | Let F be a closed proper subset of ?n and let ?* 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 ? ∈ ?* (?n) there is ${widetilde f} in {cal E}_{*}(rm R ^{n})$ which is real analytic on ?nF and such that ?a ? ¦ F = ?a ? ¦ F for any a ∈ ?0 n. For bounded ultradifferentiable functions ? we can obtain ${widetilde f}$ by means of a continuous linear operator. |
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