Analysis Seminar: "Dominating sets, spectral estimates and null-controllability"

Abstract: Let $(\Omega, \mu)$ be a measure space and let $\mathcal{F} \subset L^p(\Omega, \mu)$ be a subspace of holomorphic functions. A measurable set $E$ is said to be dominating for $\mathcal{F}$ if there exists a constant $C_E > 0$ such that $$\int_\Omega  |f|^p d\mu \le C_E \int_E |f|^p d\mu, \forall f \in \mathcal{F}.$$

In this talk, I will start giving an overview of the results concerning dominating sets for classical spaces of holomorphic functions. Then, I will explain how this question is related to certain spectral inequalities that play a central role in the null controllability of parabolic equations.

Host: Walton Green