Whitney's extension theorem for generalized functions

Abstract

If X is a subset of R n we define generalized functions on X as a direct generalization of C ∞ functions on X in Whitney's sense and of generalized functions on X when X is open. Then 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 an adaptation of a classical proof.