Browsing by Author "Richard, Christoph"

Now showing 1 - 3 of 3
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    A short guide to pure point diffraction in cut-and-project sets
    (2017) Richard, Christoph; Strungaru, Nicolae
    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 from Fourier analysis. This clarifies a common view that the diffraction of a quasicrystal is determined by the diffraction of its underlying lattice. To illustrate our approach, we will also treat a number of well-known explicitly solvable examples.
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    Modulated crystals and almost periodic measures
    (2020) Lee, Jeong-Yup; Lenz, Daniel; Richard, Christoph; Sing, Bernd; Strungaru, Nicolae
    Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyse these structures using methods from modern mathematical diffraction theory, thereby providing a coherent view over that class. Similarly to de Bruijn's analysis, we find stability with respect to almost periodic modulations.
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    Pure point diffraction and Poisson summation
    (2017) Strungaru, Nicolae; Richard, Christoph
    We show that the diffraction formula for regular model sets and the Poisson Summation Formula for the underlying lattice can be derived from one another. This is achieved using Fourier analysis of unbounded Radon measures on locally compact abelian groups, as developed by Argabright and de Lamadrid. We also discuss related diffraction results for certain classes of non-regular so-called weak model sets.