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arxiv: math/0302061 · v2 · pith:NZZKMFMKnew · submitted 2003-02-06 · 🧮 math.DS

Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra

Michael Baake (Bielefeld) , Daniel Lenz (Chemnitz) This is my paper
classification 🧮 math.DS
keywords dynamicalcompactpointpureboundeddiffractionmeasuresspectrum
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Certain topological dynamical systems are considered that arise from actions of $\sigma$-compact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point dynamical spectrum if and only if its diffraction spectrum is pure point.

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  1. On almost periodicity in crystalline measures

    math.FA 2026-05 unverdicted novelty 7.0

    Crystalline measures are almost periodic if and only if translation bounded; new constructions resolve Meyer's and Favorov's questions by exhibiting crystalline measures that are not translation bounded even as distributions.