Self-Similarities and Invariant Densities for Model Sets

  title={Self-Similarities and Invariant Densities for Model Sets},
  author={Michael Baake and Robert V. Moody},
  journal={arXiv: Mathematical Physics},
  • M. BaakeR. Moody
  • Published 3 September 1998
  • Mathematics
  • arXiv: Mathematical Physics
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of averaging operators and invariant densities on model sets. We prove that invariant densities exist and that they produce absolutely continuous invariant measures in internal space. We study the invariant densities and their relationships to diffraction, continuous… 


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