On the Fourier analysis of measures with Meyer set support

DOI10.1016/j.jfa.2019.108404zbMath1432.43001arXiv1807.03815OpenAlexW2843834306WikidataQ126800925 ScholiaQ126800925MaRDI QIDQ2286471

Nicolae Strungaru

Publication date: 22 January 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.03815

zbMATH Keywords

Fourier transformMeyer setsEberlein decompositionalmost periodic measures

Mathematics Subject Classification ID

Diffraction, scattering (78A45) Measures on groups and semigroups, etc. (43A05) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (13)

Eberlein decomposition for PV inflation systems ⋮ On the (dis)continuity of the Fourier transform of measures ⋮ ON HIGHER DIMENSIONAL ARITHMETIC PROGRESSIONS IN MEYER SETS ⋮ Fourier transformable measures with weak Meyer set support and their lift to the cut-and-project scheme ⋮ Spectral properties of substitutions on compact alphabets ⋮ On eigenmeasures under Fourier transform ⋮ A note on tempered measures ⋮ Why do (weak) Meyer sets diffract? ⋮ Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition ⋮ Modulated crystals and almost periodic measures ⋮ On norm almost periodic measures ⋮ Uniqueness theorem for Fourier transformable measures on LCA groups ⋮ On arithmetic progressions in model sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples
• Diffraction theory and almost periodic distributions
• On weak model sets of extremal density
• Pure point spectrum for measure dynamical systems on locally compact Abelian groups
• Deformation of Delone dynamical systems and pure point diffraction
• Pure point diffraction and Poisson summation
• Periods and factors of weak model sets
• Almost periodic measures and long-range order in Meyer sets
• On diffraction by aperiodic structures
• Meyer's concept of quasicrystal and quasiregular sets
• Quasicrystals and Poisson's summation formula
• Fourier quasicrystals and discreteness of the diffraction spectrum
• Pure point diffraction and cut and project schemes for measures: the smooth case
• On weighted Dirac combs supported inside model sets
• Squirals and beyond: substitution tilings with singular continuous spectrum
• A short guide to pure point diffraction in cut-and-project sets
• Fourier analysis of unbounded measures on locally compact abelian groups
• Point Sets and Dynamical Systems In the Autocorrelation Topology
• On weakly almost periodic measures
• Dynamics on the graph of the torus parametrization
• Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra
• Diffraction of Weighted Lattice Subsets
• Weighted Dirac combs with pure point diffraction
• On the Bragg Diffraction Spectra of a Meyer Set
• Almost Periodic Measures and their Fourier Transforms
• Almost Periodic Pure Point Measures
• Aperiodic Order
• Almost periodic measures
• Measures with locally finite support and spectrum

This page was built for publication: On the Fourier analysis of measures with Meyer set support