Uncertainty relations and applications in spectral and control theory

TL;DR

This paper discusses the theoretical foundations of uncertainty relations and explores their applications in spectral and control theory, emphasizing operator analysis on discrete spaces.

Contribution

It provides a comprehensive overview of uncertainty principles and demonstrates their relevance to spectral analysis and control problems in discrete operator settings.

Findings

Uncertainty relations are linked to spectral properties of operators.

Applications include spectral characterization and control system analysis.

Theoretical insights facilitate new approaches in discrete spectral theory.

Abstract

This is an extended abstract for the Oberwolfach Workshop 2101b \emph{Geometry, Dynamics and Spectrum of Operators on Discrete Spaces} organized by David Damanik, Matthias Keller, Tatiana Smirnova-Nagnibeda, and Felix Pogorzelski. It took place in online format from 3rd to 9th January 2021.