Constraints on pure point diffraction on aperiodic point patterns of finite local complexity*

We consider the pure point part of the diffraction on families of aperiodic point sets obeying common local rules. It is shown that imposing such rules results in linear constraints on the partial diffraction amplitudes. These relations can be explicitly derived from the geometry of the prototile space representing the local rules.

Automated summary

This paper investigates the pure point part of the diffraction of aperiodic point sets obeying common local rules and demonstrates that imposing such rules leads to linear constraints on the partial diffraction amplitudes.