Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774797 | Journal of Mathematical Analysis and Applications | 2017 | 9 Pages |
Abstract
We present a beautiful but relatively unknown theorem that every differentiable function f:PâR, with PâR being closed, admits differentiable extension F:RâR. We present an elementary proof of this result based on a construction sketched in a hard-to-access 1923 paper [4] of V. JarnÃk. Using this construction, we also obtain an elegant version of Whitney extension theorem characterizing when such an f admits continuously differentiable extension.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Monika Ciesielska, Krzysztof Chris Ciesielski,