Pure point diffraction and cut and project schemes for measures: the smooth case

DOI10.1007/s00209-006-0077-0zbMath1129.28003arXivmath/0603453OpenAlexW3103374005MaRDI QIDQ2385015

Christoph Richard, Daniel H. Lenz

Publication date: 11 October 2007

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603453

zbMATH Keywords

equidistributionaperiodic ordercut and project

Mathematics Subject Classification ID

Related Items (28)

Eberlein decomposition for PV inflation systems ⋮ Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks ⋮ Dynamical properties of almost repetitive Delone sets ⋮ On sampling and interpolation by model sets ⋮ Fourier transformable measures with weak Meyer set support and their lift to the cut-and-project scheme ⋮ Pure point diffraction and Poisson summation ⋮ On eigenmeasures under Fourier transform ⋮ Delone dynamical systems and spectral convergence ⋮ Why do (weak) Meyer sets diffract? ⋮ Stationary processes and pure point diffraction ⋮ Periods and factors of weak model sets ⋮ A short guide to pure point diffraction in cut-and-project sets ⋮ Modulated crystals and almost periodic measures ⋮ On weakly almost periodic measures ⋮ On the Fourier Transformability of Strongly Almost Periodic Measures ⋮ On norm almost periodic measures ⋮ Spectral notions of aperiodic order ⋮ Dynamics on the graph of the torus parametrization ⋮ On weak model sets of extremal density ⋮ Random fields on model sets with localized dependency and their diffraction ⋮ On the Fourier analysis of measures with Meyer set support ⋮ Pure point spectrum for measure dynamical systems on locally compact Abelian groups ⋮ Pure point/continuous decomposition of translation-bounded measures and diffraction ⋮ On pattern entropy of weak model sets ⋮ A note on measures vanishing at infinity ⋮ Spectral and arithmetic structures in aperiodic order ⋮ Leptin densities in amenable groups ⋮ On arithmetic progressions in model sets

Cites Work

• Deformation of Delone dynamical systems and pure point diffraction
• Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks
• Substitution dynamical systems - spectral analysis
• Quasicrystals and discrete geometry. Proceedings of the 1995 fall programme at The Fields Institute, Toronto, Canada
• Pure point dynamical and diffraction spectra
• Diffraction and Palm measure of point processes
• On diffraction by aperiodic structures
• Quasicrystals and almost periodicity
• Spectral theory and x-ray diffraction
• The torus parametrization of quasiperiodic LI-classes
• Dynamics of self-similar tilings
• Point Sets and Dynamical Systems In the Autocorrelation Topology
• Directions in Mathematical Quasicrystals
• Uniform Distribution in Model Sets
• Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra
• Weighted Dirac combs with pure point diffraction
• Dense Dirac combs in Euclidean space with pure point diffraction
• Almost periodic measures
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