Differentiable extension theorem: a lost proof of V. Jarnik


Monika Ciesielska and Krzysztof Chris Ciesielski

J. Math. Anal. Appl. 454(2) (2017) 883-890.

We present a beautiful but relatively unknown theorem that every differentiable function f from a closed subset of P R into R admits differentiable extension F:R-->R. We present an elementary proof of this result based on a construction sketched in a hard-to-access 1923 paper of V. Jarnik. Using this construction, we also obtain an elegant version of Whitney extension theorem characterizing when such an f admits continuously differentiable extension.

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Last modified June 6, 2017.