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Whenever the defining sequence of a Carleman ultraholomorphic class (in thesense of H. Komatsu) is strongly regular and associated with a proximate order,flat functions are constructed in the class on sectors of optimal opening. Asconsequences, we obtain analogues of both Borel-Ritt-Gevrey theorem andWatson's lemma in this general situation.

Flat functions in Carleman ultraholomorphic classes via proximate orders