论文标题
通过紧密的Gabor框架的磁性伪差异算子的矩阵表示
Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames
论文作者
论文摘要
在本文中，我们使用\ cite {fg-97，g-06}中的一些想法，并考虑$ \ mathbb {r}^d $（$ d \ geq1 $）上的hörmander型伪二级操作员的描述，包括磁性pseudo-diffential-diffential Operators in \ citor \ ciite cabite fimp-1 cright cabite cright imp-1，我们表明，所有这些运算符都可以用一些无限维矩阵来识别，其元素在对角线附近的元素局部强烈局限。使用此矩阵表示，可以为经典结果提供简短而优雅的证明，例如calder {ó} n-vaillancourt Theorem和Beals的换向器标准，并建立局部微量级标准。
In this paper we use some ideas from \cite{FG-97, G-06} and consider the description of Hörmander type pseudo-differential operators on $\mathbb{R}^d$ ($d\geq1$), including the case of the magnetic pseudo-differential operators introduced in \cite{IMP-1, IMP-19}, with respect to a tight Gabor frame. We show that all these operators can be identified with some infinitely dimensional matrices whose elements are strongly localized near the diagonal. Using this matrix representation, one can give short and elegant proofs to classical results like the Calder{ó}n-Vaillancourt theorem and Beals' commutator criterion, and also establish local trace-class criteria.
