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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
Posted:
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  of the Whitney jets on a closed set  to  so that the extended functions are real analytic outside  ?
- 1.
Michael
Langenbruch, Analytic extension of smooth functions, Results
Math. 36 (1999), no. 3-4, 281–296. MR 1726219
(2000i:46026)
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B.
Malgrange, Ideals of differentiable functions, Tata Institute
of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of
Fundamental Research, Bombay, 1967. MR 0212575
(35 #3446)
- 3.
Jean
Schmets and Manuel
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 1489879
(98m:46028)
- 4.
Michael
Tidten, Fortsetzungen von 𝐶^{∞}-Funktionen, welche
auf einer abgeschlossenen Menge in 𝑅ⁿ definiert sind,
Manuscripta Math. 27 (1979), no. 3, 291–312
(German, with English summary). MR 531143
(80k:58016), http://dx.doi.org/10.1007/BF01309013
- 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
- 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
 -Funktionen, welche auf einer abgeschlossenen Menge in  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:
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
Posted:
November 9, 2001
Communicated by:
N. Tomczak-Jaegermann
Article copyright:
© Copyright 2001 American Mathematical Society
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