一般Carleman超全纯类的可和性
Summability in general Carleman ultraholomorphic classes
摘要：
在扇区上的一般Carleman超全纯类的框架下，给出了可和性的定义，从而推广了J. P. Ramis从一个强正则序列的正数出发，我们构建了一个相关的解析近似的顺序和相应的内核，这使我们能够考虑适当的拉普拉斯和Borel型变换，形式和分析，其行为非常类似于经典的Gevrey的情况下。应用于研究某些矩-偏微分方程的形式解的可和性。
英文摘要：
A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing $k-$summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive numbers, we construct an associated analytic proximate order and corresponding kernels, which allow us to consider suitable Laplace and Borel-type transforms, both formal and analytic, whose behavior closely resembles that of the classical ones in the Gevrey case. An application to the study of the summability properties of the formal solutions to some moment-partial differential equations is included.
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