Quasicrystals and Poisson's summation formula

DOI10.1007/s00222-014-0542-zzbMath1402.28002arXiv1312.6884OpenAlexW3098805068MaRDI QIDQ2346752

Nir Lev, Alexander Olevskiĭ

Publication date: 4 June 2015

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6884

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05)

Related Items (38)

Fourier quasicrystals and discreteness of the diffraction spectrum ⋮ Poisson summation formulas involving the sum-of-squares function ⋮ Crystalline temperate distributions with uniformly discrete support and spectrum ⋮ Tempered distributions with discrete support and spectrum ⋮ Universal sampling and interpolation in locally compact abelian groups ⋮ Unnamed Item ⋮ Local Wiener's theorem and coherent sets of frequencies ⋮ Some properties of measures with discrete support ⋮ Discrete nonlinear Fourier transforms and their inverses ⋮ 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 ⋮ Characterisation of Meyer sets via the Freiman-Ruzsa theorem ⋮ A note on tempered measures ⋮ Perturbed interpolation formulae and applications ⋮ Crystalline measures in two dimensions ⋮ Fourier interpolation with zeros of zeta and \(L\)-functions ⋮ A short guide to pure point diffraction in cut-and-project sets ⋮ Stable polynomials and crystalline measures ⋮ Delone Sets and Dynamical Systems ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Large Fourier quasicrystals and Wiener's theorem ⋮ A geometric characterization of a class of Poisson type distributions ⋮ Poisson summation formula in Hardy spaces \(H^p(T_\Gamma )\), \(p\in (0,1\)] ⋮ Measures with locally finite support and spectrum ⋮ On the Fourier analysis of measures with Meyer set support ⋮ Fourier pairs of discrete support with little structure ⋮ Uniqueness theory for model sets, and spectral superresolution ⋮ Fourier quasicrystals and Lagarias’ conjecture ⋮ On pattern entropy of weak model sets ⋮ Doubly sparse measures on locally compact abelian groups ⋮ Wigner transform and quasicrystals ⋮ Existence of quasicrystals and universal stable sampling and interpolation in LCA groups ⋮ Bohr almost periodic sets of toral type ⋮ Universal optimality of the \(E_8\) and Leech lattices and interpolation formulas ⋮ Uniqueness theorems for Fourier quasicrystals and temperate distributions with discrete support ⋮ Fourier uniqueness pairs of powers of integers ⋮ On the duality of discrete and periodic functions

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