Pure point spectrum for measure dynamical systems on locally compact Abelian groups

DOI10.1016/j.matpur.2009.05.013zbMath1178.37008arXiv0704.2498OpenAlexW2950902938MaRDI QIDQ734313

Nicolae Strungaru, Daniel H. Lenz

Publication date: 20 October 2009

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.2498

zbMATH Keywords

diffractionpure point spectrumlocally finite measure

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (30)

Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples ⋮ Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks ⋮ Extinctions and correlations for uniformly discrete point processes with pure point dynamical spectra ⋮ Dynamical versus diffraction spectrum for structures with finite local complexity ⋮ Low complexity subshifts have discrete spectrum ⋮ Spectral theory of dynamical systems as diffraction theory of sampling functions ⋮ Delone dynamical systems and spectral convergence ⋮ Pure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicity ⋮ Why do (weak) Meyer sets diffract? ⋮ Stationary processes and pure point diffraction ⋮ Periods and factors of weak model sets ⋮ The computation of overlap coincidence in Taylor-Socolar substitution tiling ⋮ Modulated crystals and almost periodic measures ⋮ Delone Sets and Dynamical Systems ⋮ Diffraction of return time measures ⋮ On weakly almost periodic measures ⋮ On the Fourier Transformability of Strongly Almost Periodic Measures ⋮ On norm almost periodic measures ⋮ Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies ⋮ Spectral notions of aperiodic order ⋮ On weak model sets of extremal density ⋮ Close-packed dimers on the line: diffraction versus dynamical spectrum ⋮ Diffraction of stochastic point sets: Explicitly computable examples ⋮ On the Fourier analysis of measures with Meyer set support ⋮ A note on measures vanishing at infinity ⋮ Discrete spectrum for amenable group actions ⋮ Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction ⋮ Spectral and arithmetic structures in aperiodic order ⋮ An autocorrelation and a discrete spectrum for dynamical systems on metric spaces ⋮ Diffraction theory of point processes: systems with clumping and repulsion

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