论文标题
伪差算子几乎对角度化
Almost Diagonalization of Pseudodifferential Operators
论文作者
论文摘要
在这篇综述中，我们着重于伪差异操作员的几乎对角线化，并强调了时频技术在这里提供的优势。特别是，我们在Gröchenig的一份有见地的论文中追溯了他，他成功地表征了Seöstrand先前研究的一类符号，该符号通过注意到Gabor框架几乎将相应的Weyl算子对角线化。这种方法还允许提供有关相关结果的新的，更自然的证据，例如操作员的界限或符号类别的代数和维纳属性。然后，我们讨论了有关该主题的一些最新发展，即将这些结果扩展到一个更普遍的伪差操作员家族，以及与Sjöstrand的符号类别的类似结果，以及类似的结果。
In this review we focus on the almost diagonalization of pseudodifferential operators and highlight the advantages that time-frequency techniques provide here. In particular, we retrace the steps of an insightful paper by Gröchenig, who succeeded in characterizing a class of symbols previously investigated by Seöstrand by noticing that Gabor frames almost diagonalize the corresponding Weyl operators. This approach also allows to give new and more natural proofs of related results such as boundedness of operators or algebra and Wiener properties of the symbol class. Then, we discuss some recent developments on the theme, namely an extension of these results to a more general family of pseudodifferential operators and similar outcomes for a symbol class closely related to Sjöstrand's one.
