Flat functions in Carleman ultraholomorphic classes via proximate orders

preprint2014arXivOpen access

Abstract

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

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