Dynamical Approaches to Spectral Theory of Operators

This lecture explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials. It covers a brief history of the topic, including key developments by Goldshad-Molchanov, Pastur, and others. The lecture delves into the survey by D. Fillman, discussing ergodic and almost periodic aspects. It also touches on the evolution of Schrödinger equations and the concept of self-adjoint operators. Various examples and exercises are presented to illustrate the theoretical concepts discussed.