Flat functions in Carleman ultraholomorphic classes via proximate orders
arXiv:1402.2627 · doi:10.1016/j.jmaa.2014.01.083
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.
22 pages. arXiv admin note: text overlap with arXiv:1402.1669
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