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Maximal growth of the Stein-Wainger oscillatory integral
We determine the optimal growth of the Stein--Wainger oscillatory integral for every Denjoy--Carleman class defined by a positive log-convex sequence. Quasianalyticity is equivalent to boundedness in $λ$ for every fixed phase in the class. In the nonquasianalytic case, an explicit formula in the def
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