Restrictions of smooth functions to a closed subset
Classical Analysis and ODEs
2011-02-15 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.math/0312226,
title = {Restrictions of smooth functions to a closed subset},
author = {Shuzo Izumi},
journal= {arXiv preprint arXiv:math/0312226},
year = {2011}
}
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16 pages