Abstract. Let C M denote a Denjoy-Carleman class of C ∞ functions (for a given logarithmically-convex sequence M = (M n )). We construct: (1) a function in C M ((−1, 1)) which is nowhere in any smaller class; (2) a function on R which is formally C M at every point, but not in C M (R); (3) (under the assumption of quasianalyticity) a smooth function on R p (p ≥ 2) which is C M on every C M curve, but not in C M (R p ).
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