论文标题
通过有限操作员的单侧迭代框架
Frames via Unilateral Iterations of a Bounded Operator
论文作者
论文摘要
由于最近在动态抽样方面的工作的动机，我们证明了在可分开且无限维的希尔伯特空间中的框架的必要条件，以接纳$ \ {t^{n}φ\} _ {n \ geq 0} $，并在b（h）$中$ t \。此外，所有向量的表征$ \ {t^{n}φ\} _ {n \ geq 0} $是提供b（h）$的某些$ t \的框架。还给出了Riesz框架操作员表示的一些辅助结果。
Motivated by recent work in Dynamical Sampling, we prove a necessary and sufficient condition for a frame in a separable and infinite-dimensional Hilbert space to admit the form $\{T^{n} φ\}_{n \geq 0}$ with $T \in B(H)$. Also, a characterization of all the vectors $φ$ for which $\{T^{n} φ\}_{n \geq 0}$ is a frame for some $T \in B(H)$ is provided. Some auxiliary results on operator representations of Riesz frames are given as well.
