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- W2956283575 abstract "We characterize the real valued functions f defined on perfect subsets P of R which admit n-times differentiable extensions F:R→R. In this characterization no continuity of F(n) is imposed. In particular, it generalizes Jarník's Extension Theorem, according to which f admits differentiable extension F:R→R if, and only if, f is differentiable. The new characterization is also closely related to the Whitney's Extension Theorem, which characterizes partial maps f admitting n-times differentiable extensions F:R→R with continuous nth derivative F(n). We also provide an elegant description of a linear extension operator Tn:C(P)→C(R) such that Tn(f)∈Dn(R) for every Dn(R)-extendable f∈C(P) and Tn(f)∈Cn(R) whenever f∈C(P) is Cn(R)-extendable." @default.
- W2956283575 created "2019-07-23" @default.
- W2956283575 creator A5010025930 @default.
- W2956283575 date "2019-11-01" @default.
- W2956283575 modified "2023-09-27" @default.
- W2956283575 title "Smooth extension theorems for one variable maps" @default.
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- W2956283575 doi "https://doi.org/10.1016/j.jmaa.2019.07.030" @default.
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