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Annales Henri Poincaré

, Volume 18, Issue 12, pp 3903–3931 | Cite as

Pure Point Diffraction and Poisson Summation

  • Christoph Richard
  • Nicolae StrungaruEmail author
Article

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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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department für MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Department of Mathematical SciencesMacEwan UniversityEdmontonCanada
  3. 3.Department of MathematicsTrent UniversityPeterboroughCanada
  4. 4.Institute of Mathematics “Simion Stoilow”BucharestRomania

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