论文标题
通过加权矩阵扩展Gevrey规律性
Extended Gevrey regularity via weighted matrices
论文作者
论文摘要
本文的主要目的是比较研究Gevrey空间$ \ MATHCAL G_T（U）$与平滑功能空间$ C^{\ infty}（u）$之间空间之间空间之间空间的两种方法。 Komatsu风格的第一种方法基于两个参数序列的属性$ m_p = p^{τp^σ} $，$τ> 0 $，$σ> 1 $。另一个使用某些权重函数定义的重量矩阵。我们通过对矩阵参数采取投影限制来证明相应空间的等效性，而在roumieu案例中，我们需要考虑一个更大的空间作为扩展Gevrey类的电感限制的空间。
The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces $\mathcal G_t (U)$ and the space of smooth functions $C^{\infty}(U)$. The first approach in the style of Komatsu is based on the properties of two parameter sequences $M_p=p^{τp^σ}$, $τ>0$, $σ>1$. The other one uses weight matrices defined by certain weight functions. We prove the equivalence of the corresponding spaces in the Beurling case by taking projective limits with respect to matrix parameters, while in the Roumieu case we need to consider a larger space then the one obtained as the inductive limit of extended Gevrey classes.
