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Which Meyer sets are regular model sets? A characterization via almost periodicity

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arxiv 2410.22536 v1 pith:Y2XB7KA6 submitted 2024-10-29 math-ph math.CAmath.DSmath.MP

Daniel Lenz , Christoph Richard , Nicolae Strungaru This is my paper · ORCID
classification math-phmath.CAmath.DSmath.MP
keywords almostperiodicmeyermodelregularsetscompactpattern
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abstract

In 2012, Meyer introduced the notions of generalized almost periodic measure and almost periodic pattern and proved that regular model sets in Euclidean space are almost periodic patterns. Here, we prove the converse in a slightly more general setting. Specifically, we show that a Meyer set in any $\sigma$-compact locally compact abelian group is a regular model set if and only if it is an almost periodic pattern.

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  1. Twice Fourier transformable measures and diffraction theory

    math-ph 2024-11 accept novelty 4.0 of 10

    A measure is twice Fourier transformable exactly when it is translation bounded and AG transformable, and this powers new Poisson summation and pure point diffraction formulas for weighted model sets.

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