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Pure Point Diffraction and Poisson Summation

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Abstract

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.

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Authors and Affiliations

  1. Department für Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058, Erlangen, Germany

    Christoph Richard

  2. Department of Mathematical Sciences, MacEwan University, 10700 104 Avenue, Edmonton, AB, T5J 4S2, Canada

    Nicolae Strungaru

  3. Department of Mathematics, Trent University, Peterborough, ON, Canada

    Nicolae Strungaru

  4. Institute of Mathematics “Simion Stoilow”, Bucharest, Romania

    Nicolae Strungaru

Authors
  1. Christoph Richard
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  2. Nicolae Strungaru
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Correspondence to Nicolae Strungaru.

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Communicated by Jean Bellissard.

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Richard, C., Strungaru, N. Pure Point Diffraction and Poisson Summation. Ann. Henri Poincaré 18, 3903–3931 (2017). https://doi.org/10.1007/s00023-017-0620-z

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  • DOI: https://doi.org/10.1007/s00023-017-0620-z

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