Kinematic diffraction from a mathematical viewpoint

Abstract

various unexpected new facets. This is particularly so for systems with stochastic components. After an introduction to the mathematical tools, we briefly discuss pure point spectra, based on the Poisson summation formula for lattice Dirac combs. This provides an elegant approach to the diffraction formulas of infinite crystals and quasicrystals. We continue by considering classic deterministic examples with singular or absolutely continuous diffraction spectra. In particular, we recall an isospectral family of structures with continuously varying entropy. We close with a summary of more recent results on the diffraction of dynamical systems of algebraic or stochastic origin. © by Oldenbourg Wissenschaftsverlag, München.