论文标题
通过动态抽样对框架表示的调查
A survey on frame representations via dynamical sampling
论文作者
论文摘要
Dynamical sampling deals with representations of a frame $\{ f_k \}_{k=1}^\infty$ as an orbit $\{ T^n φ\}_{n=0}^\infty$ of a linear and possibly bounded operator $T$ acting on the underlying Hilbert space.众所周知，操作员$ t $的有限性在框架$ \ {f_k \} _ {k = 1}^\ infty $上施加严重限制。本文的目的是介绍文献中的结果，并讨论代表框架的各种替代方法。特别地，可以通过仅使用子集$ \ {t^{t^{t^{α（k）}φ\}^\ infty_ {k = 1} $允许表示表示，可以大幅度放大所考虑帧的类别。通常，很难为标量$α（k）$和向量$φ; $指定适当的值，但是，通过接受给定的框架$ \ {f_k \} _ {k = 1}^^^\ infty $和$ \ \ \ {t^（k）（k）（k）（k）（k）（k）} n WILL wily wer we we wily we w we wer这样做。
Dynamical sampling deals with representations of a frame $\{ f_k \}_{k=1}^\infty$ as an orbit $\{ T^n φ\}_{n=0}^\infty$ of a linear and possibly bounded operator $T$ acting on the underlying Hilbert space. It is known that the desire of boundedness of the operator $T$ puts severe restrictions on the frame $\{ f_k \}_{k=1}^\infty$. The purpose of the paper is to present an overview of the results in the literature and also discuss various alternative ways of representing a frame; in particular the class of considered frames can be enlarged drastically by allowing representations using only a subset $\{ T^{α(k)} φ\}^\infty_{k=1}$ of the operator orbit $\{ T^n φ\}_{n=0}^\infty$. In general it is difficult to specify appropriate values for the scalars $α(k)$ and the vector $φ;$ however, by accepting an arbitrarily small and controllable deviation between the given frame $\{ f_k \}_{k=1}^\infty$ and $\{ T^{α(k)} φ\}_{k=1}^\infty$ we will be able to do so.
