论文标题
作为谐波函数边界值的准二元分析功能和超部分
Quasianalytic functionals and ultradistributions as boundary values of harmonic functions
论文作者
论文摘要
我们研究了非Quasianalyty类型的超端分布空间的谐波功能的边界值。作为应用程序，我们为霍曼德（Hörmander）的支持定理提供了一种新的方法。我们的主要技术工具是通过几乎谐波函数对超平不同功能的描述，这是我们在本文中介绍的概念。我们在通过重量矩阵定义的超平整类别的设置中工作。特别是，我们的结果同时适用于通过权重序列和权重函数定义的两个标准类。
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to Hörmander's support theorem for quasianalytic functionals. Our main technical tool is a description of ultradifferentiable functions by almost harmonic functions, a concept that we introduce in this article. We work in the setting of ultradifferentiable classes defined via weight matrices. In particular, our results simultaneously apply to the two standard classes defined via weight sequences and via weight functions.
