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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Analytic extension of differentiable functions defined in closed sets by means of continuous linear operators


Authors: Leonhard Frerick and Dietmar Vogt
Journal: Proc. Amer. Math. Soc. 130 (2002), 1775-1777
MSC (2000): Primary 46E10
Published electronically: November 9, 2001
MathSciNet review: 1887025
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Abstract: In this paper we solve the following problem posed by Schmets and Valdivia: Under which conditions does there exist an extension operator from the space ${\mathscr E} (F) $ of the Whitney jets on a closed set $ F \subset{\mathbb{R}} ^n $ to ${\mathscr E}({\mathbb{R}}^n)$ so that the extended functions are real analytic outside $ F $?


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Additional Information

Leonhard Frerick
Affiliation: FB Mathematik, Bergische Universität Wuppertal, Gaußstrasse 20, D–42097 Wuppertal, Germany
Email: frerick@math.uni-wuppertal.de

Dietmar Vogt
Affiliation: FB Mathematik, Bergische Universität Wuppertal, Gaußstrasse 20, D–42097 Wuppertal, Germany
Email: vogt@math.uni-wuppertal.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06260-8
PII: S 0002-9939(01)06260-8
Keywords: Whitney jets, extension operator, real analytic extension
Received by editor(s): October 18, 2000
Received by editor(s) in revised form: December 20, 2000
Published electronically: November 9, 2001
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2001 American Mathematical Society