Examples of functions $𝐶^𝑘$-extendable for each 𝑘 finite, but not $𝐶^∞$-extendable

• Autorzy: Wiesław Pawłucki
• Języki publikacji: EN

Abstrakty

EN

In Example 1, we describe a subset X of the plane and a function on X which has a $𝐶^k$-extension to the whole $ℝ^2$ for each 𝑘 finite, but has no $𝐶^∞$-extension to $ℝ^2$. In Example 2, we construct a similar example of a subanalytic subset of $ℝ^5$; much more sophisticated than the first one. The dimensions given here are smallest possible.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 44
• Numer: 1
• Strony: 183-187

Daty

wydano

1998

Twórcy

autor

Wiesław Pawłucki

• Instytut Matematyki, Uniwersytet Jagielloński,, ul. Reymonta 4, 30-059 Kraków, Poland,

Bibliografia

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