Talk by Walton Green

I will introduce the general problem of dominating sets for function spaces and discuss its connection to control theory of hyperbolic PDEs through various Paley-Weiner spaces. First, this motivates new and interesting questions in complex and harmonic analysis concerning Paneah-Logvinenko-Sereda (PLS)-type theorems. Then, these PLS theorems can be applied to study observability and energy decay of wave equations in the whole Euclidean space.

This is joint work with B. Jaye and M. Mitkovski.