Analytic Extension of Non Quasi ‐ Analytic Whitney Jets of Beurling Type

Let ( M r ) r ∈ ℕ0 be a logarithmically convex sequence of positive numbers which verifies M 0 = 1 as well as M r ≥ 1 for every r ∈ ℕ and defines a non quasi ‐ analytic class. Let moreover F be a closed proper subset of ℝ n . Then for every function f on ℝ n belonging to the non quasi ‐ analytic ( M r )‐class of Beurling type, there is an element g of the same class which is analytic on ℝ, n F and such that D α f ( x ) = D α g ( x ) for every α ∈ ℕ n 0 and x ∈ F .