论文标题
离散调制空间上的本地化操作员
Localization Operators On Discrete Modulation Spaces
论文作者
论文摘要
在本文中，我们研究了一类伪差异操作员，称为$ \ Mathbb z^n $上的时频定位运算符，该操作员依赖于符号$ς$和两个Windows函数$ G_1 $和$ G_2 $。我们在$ \ mathbb z^n \ times \ mathbb t^n $上定义了短时傅立叶变换，并在$ \ mathbb z^n $上定义了调制空间，并提供了一些基本属性。然后，我们在$ \ mathbb z^n \ times \ times \ mathbb t^n $上使用调制空间作为符号的适当类，并研究本地化操作员在$ \ mathbb z^n $上的调制空间上的界限和紧凑性。然后，我们表明这些运营商在schatten-von neumann班级中。此外，我们在$ \ Mathbb z^n $上获得了Landau-Pollak-Slepian类型操作员与本地化操作员之间的关系。最后，在符号上适当的条件下，我们证明本地化运算符是副公共，副群和傅立叶乘数。
In this paper, we study a class of pseudo-differential operators known as time-frequency localization operators on $\mathbb Z^n$, which depend on a symbol $ς$ and two windows functions $g_1$ and $g_2$. We define the short-time Fourier transform on $ \mathbb Z^n \times \mathbb T^n $ and modulation spaces on $\mathbb Z^n$, and present some basic properties. Then, we use modulation spaces on $\mathbb Z^n \times \mathbb T^n$ as appropriate classes for symbols, and study the boundedness and compactness of the localization operators on modulation spaces on $\mathbb Z^n$. Then, we show that these operators are in the Schatten--von Neumann class. Also, we obtain the relation between the Landau--Pollak--Slepian type operator and the localization operator on $\mathbb Z^n$. Finally, under suitable conditions on the symbols, we prove that the localization operators are paracommutators, paraproducts and Fourier multipliers.
