论文标题
连续和离散的动态抽样
Continuous and discrete dynamical sampling
论文作者
论文摘要
在本文中，我们研究了复杂的希尔伯特空间中无限时间的连续动态抽样问题$ \ Mathcal {H} $。我们在\ Mathcal {b}（\ Mathcal {h}）$和一组向量$ \ Mathcal {g} \ subset \ subset \ Mathcal {H Mathcal {h} $中找到了有限的线性运算符$ a \ in \ Mathcal {b}（\ Mathcal {B}（\ Mathcal {h}）的必要条件，以获得该$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t \ in [0，\ infty）} $是$ \ Mathcal {H} $的半连续框架。我们研究是否可以离散时间变量$ t $，并且仍然有$ \ MATHCAL {H} $的框架。我们还将连续迭代$ e^{ta} $在$ \ \ \ m nathcal {g}^\ prime $上的$ \ mathcal {g} $与离散迭代$（a^\ prime）^n $上的连续迭代联系起来
In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space $\mathcal{H}$. We find necessary and sufficient conditions on a bounded linear operator $A\in\mathcal{B}(\mathcal{H})$ and a set of vectors $\mathcal{G}\subset \mathcal{H}$, in order to obtain that $\{e^{tA}g\}_{g\in\mathcal{G}, t\in[0,\infty)}$ is a semi-continuous frame for $\mathcal{H}$. We study if it is possible to discretize the time variable $t$ and still have a frame for $\mathcal{H}$. We also relate the continuous iteration $e^{tA}$ on a set $\mathcal{G}$ to the discrete iteration $(A^\prime)^n$ on $\mathcal{G}^\prime$ for an adequate operator $A^\prime$ and set $\mathcal{G}^\prime\subset \mathcal{H}$.
