English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider topological dynamical systems over $${\mathbb {Z}}$$ and, more generally, locally compact, $$\sigma $$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of diffraction theory to associate an autocorrelation and a diffraction measure to any $$L^2$$-function over such a dynamical system. This diffraction measure is shown to be the spectral measure of the function. If the group has a countable basis of the topology one can also exhibit the underlying autocorrelation by sampling along the orbits. Building on these considerations we then show how the spectral theory of dynamical systems can be reformulated via diffraction theory of function dynamical systems. In particular, we show that the diffraction measures of suitable factors provide a complete spectral invariant.

Spectral theory of dynamical systems as diffraction theory of sampling functions