Department Kolloquium Winter 2023/24

Dynamical Sampling and Frames

Akram Aldroubi, Vanderbilt University: 14:30 bis 15:30 Uhr

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 H: (0.1) ( u˙(t) = Au(t) + F(t) u(0) = u0, t ∈ R+, u0 ∈ H, where t ∈ [0,∞), u : R+ → H, ˙u : R+ → H is the time derivative of u, and u0 is an initial condition. When, F = 0, A is a known (or unknown) operator, and the goal is to recover u0 from the samples {u(ti , xj )} on a sampling set {(ti , xj )}, 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 new results.