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Restrictions of smooth functions to a closed subset

Shuzo Izumi
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Abstract

We first provide an approach to the recent conjecture of Bierstone-Milman-Pawlucki on Whitney's old problem on smooth extendability of functions defined on a closed subset of a Euclidean space, using higher order paratangent bundle they introduced. For example, the conjecture is affirmative for classical fractal sets. Next, we give a sharpened form of Spallek's theorem on controllability of flatness by the values on a closed set. The multi-dimensional Vandermonde matrix plays an important role in both cases.

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Shuzo Izumi. 2003-12-11. Restrictions of smooth functions to a closed subset. https://arxiv.org/abs/math/0312226

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