Dynamical sampling is a term describing an emerging set of problems related to recovering signals and evolution operators from space-time samples. For example, consider the abstract IVP in a separable Hilbert space $\mathcal{H}$:
\begin{equation} \begin{cases} \dot{u}(t) =Au(t) + F(t)\\ u(0)=u_{0} \end{cases}\,, \end{equation} $t\in \mathbb{R}_{+},u_{0}\in \mathcal{H}$,
where $t\in [0,\infty), u : \mathbb{R}_{+} \mapsto \mathcal{H}, \dot{u} : \mathbb{R}_{+} \mapsto \mathcal{H}$ is the time derivative of $u$, and $u_0$ is an initial condition. When, $F = 0, A$ is a known (or unknown) operator, and the goal is to recover $u_0$ from the samples $\{ u(t_{i},x_{j}) \}$ on a sampling set ${(t_i, x_j )}$, we get the so called space-time sampling problems. If the goal is to identify the operator $A$, or some of its characteristics, we get the system identification problems. If instead we wish to recover $F$, we get the source term problems. In this talk, I will present an overview of dynamical sampling, and some open problems.
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