动态采样与算子迭代作用系统
Dynamical sampling and systems from iterative actions of operators
摘要：
我们回顾了最近的一些发展，并证明了新的结果框架和贝塞尔系统的形式$\{A^ng: g\in G,\, n=0,1,2,\dots \}$，其中$A$是可分复希尔伯特空间$ \mathcal{H} $上的有界线性算子和$G$是一个可数集的$ \mathcal{H} $迭代。上述迭代系统是从所谓的动态采样问题出发的。在动态采样中，在每个时间级$n$、$0\leq n< L$对未知函数$f$及其未来状态$A^nf$进行粗采样，其中$A$是驱动系统的演化算子。目标是从这些时空样本中恢复$f$。
英文摘要：
We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex Hilbert space $ \mathcal{H} $ and $G$ is a countable set of vectors in $ \mathcal{H} $. The system of iterations mentioned above was motivated from the so called dynamical sampling problem. In dynamical sampling, an unknown function $f$ and its future states $A^nf$ are coarsely sampled at each time level $n$, $0\leq n< L$, where $A$ is an evolution operator that drives the system. The goal is to recover $f$ from these space-time samples.
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。
