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

Author(s): Leonhard Frerick; Dietmar Vogt
Journal: Proc. Amer. Math. Soc. 130 (2002), 1775-1777.
MSC (2000): Primary 46E10
Posted: November 9, 2001
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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 ?

References:

1.: M. Langenbruch, Analytic extension of smooth functions, Result. Math. 36 (1999), no. 3-4, 281-296. MR 2000i:46026
2.: B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Oxford University Press, London, 1967. MR 35:3446
3.: J. Schmets, M. Valdivia, On the existence of continuous linear analytic extension maps for Whitney jets, Bull. Polish Acad. Sci. Math. 45 (1997), no. 4, 359-367. MR 98m:46028
4.: M. Tidten, Fortsetzungen von $C^\infty$ -Funktionen, welche auf einer abgeschlossenen Menge in ${\mathbb{R}}^n$ definiert sind, Manuscripta Math. 27 (1979), no. 3, 291-312. MR 80k:58016
5.: H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), no. 1, 63-89. CMP 95:18

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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: 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
Posted: November 9, 2001
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2001, American Mathematical Society


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