论文标题
超过分布空间中的边界值与扩展的Gevrey规律性有关
Boundary values in ultradistribution spaces related to extended Gevrey regularity
论文作者
论文摘要
遵循众所周知的Beurling和Roumieu超级分布理论，我们将超级分布的新空间作为测试函数的双空间，这些空间与Infinity的对数型生长的相关功能相对应。在给定的框架中，我们证明具有相应的对数增长率对实际领域的分析函数的边界值是超级分布。为此目的的基本条件是经典超级分布理论中的条件$（M.2）$，被新的$ \ widetilde {（M.2）} $取代。因此，在证明中执行了新技术。作为应用程序，我们讨论相应的波前集。
Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth rate towards the real domain are ultradistributions. The essential condition for that purpose, condition $(M.2)$ in the classical ultradistribution theory, is replaced by the new one, $\widetilde{(M.2)}$. For that reason, new techniques were performed in the proofs. As an application, we discuss the corresponding wave front sets.
