论文标题
混合贝尔林环境中的Borel地图
The Borel map in the mixed Beurling setting
论文作者
论文摘要
Borel图将其平滑函数带到其无限的衍生物射流（零）。我们研究了这张地图在非常通用的环境中限制对超平稳性类型类型的限制，该类型涵盖了经典的Denjoy-Carleman和Braun-Meise-Taylor类。更确切地说，我们表征当一个类的Borel图像按照定义类的两个权重覆盖另一类的序列空间时。我们提出了两个独立的解决方案，一种是通过减少roumieu案例，另一个是通过对涉及的fréchet空间进行双重化，phragmén-lindelöf定理以及Hörmander对$ \ bar {\ partial} $ - 问题的解决方案的解决方案。
The Borel map takes a smooth function to its infinite jet of derivatives (at zero). We study the restriction of this map to ultradifferentiable classes of Beurling type in a very general setting which encompasses the classical Denjoy-Carleman and Braun-Meise-Taylor classes. More precisely, we characterize when the Borel image of one class covers the sequence space of another class in terms of the two weights that define the classes. We present two independent solutions to this problem, one by reduction to the Roumieu case and the other by dualization of the involved Fréchet spaces, a Phragmén-Lindelöf theorem, and Hörmander's solution of the $\bar{\partial}$-problem.
