论文标题
在具有单一结构的连续框架的分析操作员范围内进行采样
Sampling in the range of the analysis operator of a continuous frame having unitary structure
论文作者
论文摘要
我们在具有统一结构的连续框架的分析操作员的范围内建立了常规抽样理论。统一结构与可分离的希尔伯特空间上局部紧凑的阿贝尔群的单一表示有关。样品是通过合适的离散卷积系统来定义的，该系统概括了一些常规的采样设置；这里的常规采样意味着样品是在可数的离散子组中进行的。
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable Hilbert space. The samples are defined by means of suitable discrete convolution systems which generalize some usual sampling settings; here regular sampling means that the samples are taken at a countable discrete subgroup.
