论文标题
通过快速增长序列定义的某些超质体类别的扩展操作员
Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
论文作者
论文摘要
虽然在一个领域中将函数发送到其一系列渐近扩展中的渐近borel映射已知在与快速增长序列相关的超纯态类别的框架内的任意开放量被过多，但在这种情况下没有构造扩展运算符的一般程序。我们确实为S.尽管用他们的话说，这些类是“超越Gevrey的规律性”，但在某些情况下，它们将稳定性的特性保持在差分之下，这对我们的技术至关重要，这对于我们的技术至关重要，基于正式的Borel和截断的Laplace样转换，具有合适的内核。
While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is no general procedure to construct extension operators in this case. We do provide such operators in complex sectors for some particular classes considered by S.~Pilipovi{ć}, N.~Teofanov and F.~Tomi{ć} in the ultradifferentiable setting. Although these classes are, in their words, "beyond Gevrey regularity", in some cases they keep the property of stability under differentiation, which is crucial for our technique, based on formal Borel- and truncated Laplace-like transforms with suitable kernels.
