论文标题
在$ l^2（\ mathbb {r}^d）$上的Hilbert-Schmidt操作员某些子空间中的平均采样
Average sampling in certain subspaces of Hilbert-Schmidt operators on $L^2(\mathbb{R}^d)$
论文作者
论文摘要
操作员翻译的概念允许考虑希尔伯特 - 史密特运算符类中的移位不变子空间的类似物。因此，我们将平均抽样的概念扩展到了这种新设置，并获得了相应的采样公式。这里的要点是使用Weyl Transform的使用，这是平方集成函数在相位空间中的空间之间的统一映射，$ \ MATHBB {r}^d \ times \ times \ times \ wideHat {\ sathbb {r}}^d $与希尔伯特·希尔伯特（Hilbert-schmidt）的$ l^2（$ l^2（p）采样结果。
The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the corresponding sampling formulas. The key point here is the use of the Weyl transform, a unitary mapping between the space of square integrable functions in the phase space $\mathbb{R}^d\times \widehat{\mathbb{R}}^d$ and the Hilbert space of Hilbert-Schmidt operators on $L^2(\mathbb{R}^d)$, which permits to take advantage of some well established sampling results.
