Whitney's extension theorem for generalized functions (Q1082587)

The definition of generalized functions from the second author extends to any non necessarily open subset X of \(R^ n\). We prove that, if X is closed, any generalized function on X may be extended as a generalized function on \(R^ n\), which is a Whitney's extension theorem for generalized functions. This result generalizes Borel's theorem for generalized functions already proved by the same authors. The proof is obtained from an analysis of a proof due to M. R. Hestenes of the classical Whitney's extension theorem. In the case X is a closed half space we have a simple proof of this theorem following \textit{R. T. Seeley}'s proof [Proc. Am. Math. Soc. 15, 625-626 (1964; Zbl 0127.284)].