# Talk by Michela Egidi

On April 28th, 2021, Dr. Michela Egidi (Ruhr-Universität Bochum) gave a talk about "**Spectral inequalities and thick sets: an abstract Logvinenko-Sereda type theorem**" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.

## Abstract

We consider functions in a spectral subspace associated with a finite energy level of a lower semi-bounded self-adjoint operator on an Euclidean $ L^2 $-space and we show that the notion of thick set is sufficient to bound the total $ L^2 $-norm by the $ L^2 $-norm on a subset times a constant depending on the energy level and the subset itself, obtaining an inequality known as spectral inequality or unique continuation principle. The proof is based on complex analytical methods used by Kovrijkine in the context of Fourier Analysis to sharpen a theorem of Logvinenko and Sereda.

The talk is based on a joint work with Albrecht Seelmann.