On the algebra of functions $\mathcal {C}^k$-extendable for each $k$ finite
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Abstract:
For each positive integer $l$ we construct a $\mathcal C^l$-function of one real variable, the graph $\Gamma$ of which has the following property: there exists a real function on $\Gamma$ which is $\mathcal C^k$-extendable to $\mathbb {R}^2$, for each $k$ finite, but it is not $\mathcal C^{\infty }$-extendable.References
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Additional Information
- Wiesław Pawłucki
- Affiliation: Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. Reymonta 4, 30-059 Kraków, Poland
- Email: Wieslaw.Pawlucki@im.uj.edu.pl
- Received by editor(s): October 13, 2003
- Published electronically: September 8, 2004
- Additional Notes: This research was partially supported by the KBN grant 5 PO3A 005 21 and the European Community IHP-Network RAAG (HPRN-CT-2001-00271)
- Communicated by: David Preiss
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 481-484
- MSC (2000): Primary 26E10; Secondary 32S05, 32B20
- DOI: https://doi.org/10.1090/S0002-9939-04-07756-1
- MathSciNet review: 2093071