Let ( M r ) r e ~o be a logarithmically convex sequence of positive numbers which verifies M,, = 1 as well as M, 2 1 for every r E IN and defines a non quasianalytic class. Let moreover F be a closed proper subset of R". Then for every function f on IR" belonging to the non quasi -analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on IR" \ F and
1, Introduction and statement of the result
In [13], H. WHITNEY has established that every C" -Whitney jet on a closed subset F of R" has a C" -extension on IR" which is analytic on IR" \ F. Since then several authors have considered the extension problem of jets in different situations; here are references to some of them [l], (21, [311 [4] [7], [lo], (111 and [12]with in [3), a discussion of the previous literature on the subject. In particular] one finds a) in [l] (resp. (41 and [ll]) conditions on the weight w (resp. on the sequence
( M r ) , . E ~o )
under which the restriction map
is surjective for every compact subset K of IRn, tinuous linear right inverse.
(My) -Whitney jets of Beurling type. b) in (71 (resp. [4] and [ll]) conditions under which this restriction map has a con-In this paper, we are going to consider this problem in the case of non quasianalytic In order to make this statement more precise, let us introduce some notations.