Flat functions in Carleman ultraholomorphic classes via proximate orders

作者：Sanz Javier^*

来源：Journal of Mathematical Analysis and Applications, 2014, 415(2): 623-643.

DOI：10.1016/j.jmaa.2014.01.083

• Carleman ultraholomorphic classes
• Asymptotic expansions
• Proximate order
• Borel-Ritt-Gevrey theorem
• Watson%26apos
• s lemma
• Laplace transform
• Extension operators

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%26apos;s lemma in this general situation.

• 出版日期2014-7-15