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Circular Symmetry of Pinwheel Diffraction
Abstract.A method is given for explicitly determining the autocorrelation of the pinwheel tiling by use of the substitution system generating the tiling. Using this a new proof of the circularExpand
Almost Periodic Measures and Long-Range Order in Meyer Sets
The main result of this paper is that the diffraction pattern of any Meyer set with a well-defined autocorrelation has a relatively dense set of Bragg peaks. In the second part of the paper weExpand
Almost Periodic Measures and Meyer Sets
In the first part, we construct a cut and project scheme from a family $\{P_\varepsilon\}$ of sets verifying four conditions. We use this construction to characterize weighted Dirac combs defined byExpand
On weak model sets of extremal density
The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the k-th power-free integers, or related systems. They belong to the class ofExpand
Point Sets and Dynamical Systems In the Autocorrelation Topology
Abstract This paper is about the topologies arising from statistical coincidence on locally finite point sets in locally compact Abelian groups $G$ . The first part defines a uniform topologyExpand
On weighted Dirac combs supported inside model sets
In this paper we prove that given a weakly almost periodic measure μ supported inside some model set with closed window W, then the strongly almost periodic component and the null weakly almostExpand
On the Bragg Diffraction Spectra of a Meyer Set
Abstract Meyer sets have a relatively dense set of Bragg peaks, and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate theExpand
Almost Periodic Pure Point Measures
A short guide to pure point diffraction in cut-and-project sets
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem fromExpand
On the Fourier analysis of measures with Meyer set support
Abstract In this paper we show the existence of the generalized Eberlein decomposition for Fourier transformable measures with Meyer set support. We prove that each of the three components is alsoExpand