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 Γ of which has the following property: there exists a real function on Γ which is$\mathcal{C}^{k}$-extendable to R2, for each k finite, but it is not C∞-extendable.

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Published in:Proceedings of the American Mathematical Society 2005-02, Vol.133 (2), p.481-484
Main Author: Wiesław Pawłucki
Format: Article
Language:English
Subjects:
Algebra
Integers
Mathematical functions
Mathematical theorems
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description For each positive integer l we construct a$\mathcal{C}^l$-function of one real variable, the graph Γ of which has the following property: there exists a real function on Γ which is$\mathcal{C}^{k}$-extendable to R2, for each k finite, but it is not C∞-extendable.
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source JSTOR Archival Journals; American Mathematical Society Publications (Freely Accessible)
subjects Algebra
Integers
Mathematical functions
Mathematical theorems
title On the Algebra of Functions$\mathcal{C}^k$-Extendable for Each k Finite
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