论文标题
具有多维中心的降低的海森堡组的本地化操作员和Weyl变换
Localization Operator and Weyl Transform on Reduced Heisenberg Group with Multi-dimensional Center
论文作者
论文摘要
在本文中，我们研究了具有多维中心$ \ Mathcal {G} $的Heisenberg Group的两种不同类型的操作员，即定位运算符和Weyl Transform。组$ \ Mathcal {g} $是一个非各向异性海森伯格组的商组，其中心由其中心子组提供了多维中心$ \ MATHCAL {H}^m $。首先，我们使用$ \ Mathcal {g} $上的小波变换来定义本地化操作员，并为本地化操作员获取产品公式。 接下来，我们将与操作员值符号上的$ \ Mathcal {g} $上的Wigner变换相关联的Weyl变换。最后，我们已经证明，当操作员价值符号位于$ l^p，1 \ leq p \ leq 2，$时，Weyl变换不仅是一个有界的操作员，而且是紧凑的操作员，当$ p> 2 $时，它是无绑定的操作员。
In this article, we study two different types of operators, the localization operator and Weyl transform, on the reduced Heisenberg group with multidimensional center $\mathcal{G}$. The group $\mathcal{G}$ is a quotient group of non-isotropic Heisenberg group with multidimensional center $\mathcal{H}^m$ by its center subgroup. Firstly, we define the localization operator using a wavelet transform on $\mathcal{G}$ and obtain the product formula for the localization operators. Next, we define the Weyl transform associated to the Wigner transform on $\mathcal{G}$ with the operator-valued symbol. Finally, we have shown that the Weyl transform is not only a bounded operator but also a compact operator when the operator-valued symbol is in $L^p,1\leq p\leq 2,$ and it is an unbounded operator when $p>2$.
