22. Spectral Properties of Dynamical Systems

In this lecture we discuss a “functional analytic” interpretation of mixing and weakly mixing for measure-preserving dynamical systems.

The last part of this lecture is non-examinable, since it uses a version of the Spectral Theorem that you probably have not seen before^[1].

Next lecture we will move back into the topological world, and investigate when^[2] a topological dynamical system on a compact metric space admits an invariant measure (i.e. a measure for which the system becomes measure-preserving).