Pure point diffraction and cut and project schemes for measures: The smooth case

Details Pure point diffraction and cut and project schemes for measures: The smooth case Pure point diffraction and cut and project schemes for measures: The smooth case

2006-03-18

arxiv.org/abs/math/0603453v1

Mathematische Zeitschrift (Volume 256) Pages 347-378, 2007

Mathematics

Dynamical Systems

30 pages

Scientific paper

10.1007/s00209-006-0077-0

We present cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic images of the underlying torus. In particular, they are strictly ergodic with pure point spectrum and continuous eigenfunctions. Their diffraction can be calculated explicitly. Our results cover and extend corresponding earlier results on dense Dirac combs and continuous weight functions with compact support. They also mark a clear difference in terms of factor maps between the case of continuous and non-continuous weight functions.

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