On the algebra of functions \mathcal{C}^k-extendable for each k finite

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.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-02, Vol.133 (2), p.481-484
Main Author: Wieslaw Pawlucki
Format: Article
Language:English
Subjects:
Algebra
Integers
Mathematical functions
Mathematical theorems
Online Access:Get full text
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Description
Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-04-07756-1