Restrictions of smooth functions to a closed subset

Details Restrictions of smooth functions to a closed subset Restrictions of smooth functions to a closed subset

2003-12-11

arxiv.org/abs/math/0312226v2

Ann. Inst. Fourier, Grenoble vol 54, 6 2004, 1811-1826

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

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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