On Non Quasi-Analytic Classes of Functions and the Space of Whitney Jets of Class M

Abstract

We investigate some problems on the space E M (Ω) (resp. E[ω] (Ω)) of ultradifferentiable functions of class \( M = {\left( {{M_k}} \right)_{k \in {N_0}\left( { = N \cup \left\{ 0 \right\}} \right)}} \) (resp. Beurling, Roumieu type) and that of E M (K) (resp. E [ω](K)) of Whitney jets of class M (resp. Beurling, Roumieu type) on a compact set K in R n. Also we consider the problems on non quasi-analytic classes of functions. Here M (resp. [ω]) stands for (M k ) or {M k } (resp. (ω) or {ω}.