关于一个（不再）新的Segal代数--Feichtinger代数的综述
On a (no longer) new Segal algebra - a review of the Feichtinger algebra
摘要：
自1979年发明以来，Feichtinger代数已成为一个非常有用的巴拿赫空间的功能与应用程序中的时间-频率分析，理论的伪微分算子和其他几个主题。它是很容易定义的局部紧阿贝尔群，并在比较施瓦茨（-Bruhat）空间，Feichtinger代数允许更一般的结果与更容易的证明。本文对Feichtinger代数的理论及其有利性质作了线性的、全面的推导。这些材料提供了一个进入这个主题的切入点，但它也会给专家带来新的见解。本文的一个主要目标是显示在文献中已知的Feichtinger代数的许多不同的特征的等价性。这项任务自然指导纸通过基本性质的职能，属于空间，在运营商对它和方面的对偶空间。进一步的结果包括一个似乎被遗忘的定理赖特对运营商产生的巴拿赫空间同构的Feichtinger代数;一个新的鉴定的Feichtinger代数作为唯一的巴拿赫空间在$L^{1}$与某些性质;和核定理的Feichtinger代数。包括理论的发展，其应用和相关的函数空间建设的历史描述。
英文摘要：
Since its invention in 1979, the Feichtinger algebra has become a very useful Banach space of functions with applications in time-frequency analysis, the theory of pseudo-differential operators and several other topics. It is easily defined on locally compact abelian groups and, in comparison with the Schwartz(-Bruhat) space, the Feichtinger algebra allows for more general results with easier proofs. This review paper gives a linear and comprehensive deduction of the theory of the Feichtinger algebra and its favourable properties. The material gives an entry point into the subject, but it will also give new insight to the expert. A main goal of this paper is to show the equivalence of the many different characterizations of the Feichtinger algebra known in the literature. This task naturally guides the paper through basic properties of functions that belong to the space, over operators on it and to aspects of its dual space. Further results include a seemingly forgotten theorem by Reiter on operators which yield Banach space isomorphisms of the Feichtinger algebra; a new identification of the Feichtinger algebra as the unique Banach space in $L^{1}$ with certain properties; and the kernel theorem for the Feichtinger algebra. A historical description of the development of the theory, its applications and related function space constructions is included.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
