Orateur
Description
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 $\mathcal{H}$:
(0.1) $\left\{\begin{matrix}
\dot{u}(t) & =Au(t) & + F(t)\\
u(0)&=u_{0} &
\end{matrix}\right.$ $\; \; \;$ $t\in \mathbb{R}_{+},u_{0}\in \mathcal{H}$,
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 u0 from the samples $\left \{ u(t_{i},x_{j}) \right \}$ 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.
