Pure point diffraction and Poisson summation

Christoph Richard; Nicolae Strungaru

Pure point diffraction and Poisson summation

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arxiv 1512.00912 v3 pith:V3CUBLJY submitted 2015-12-03 math-ph math.MP

Christoph Richard , Nicolae Strungaru This is my paper · ORCID

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keywords diffractionformulamodelpoissonsetssummationabelianachieved

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We prove that the diffraction formula for regular model sets is equivalent to the Poisson Summation Formula for the underlying lattice. This is achieved using Fourier analysis of unbounded measures on locally compact abelian groups as developed by Argabright and de Lamadrid. We also obtain diffraction results for certain classes of non-regular so-called weak model sets.

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Pure point measures with sparse support and sparse Fourier--Bohr support
math.MG 2019-08 accept novelty 7.0 of 10

Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.

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