Existence of quasicrystals and universal stable sampling and interpolation in LCA groups

DOI10.1090/tran/7723zbMath1431.42052arXiv1611.05804OpenAlexW2963158516MaRDI QIDQ5234502

Basarab Matei, Jorge Antezana, Elona Agora, Carlos A. Cabrelli

Publication date: 26 September 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05804

zbMATH Keywords

quasicrystalslocally compact abelian groupsPoisson measuresLandau-Beurling's densitiesuniversal sampling and interpolation

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) General harmonic expansions, frames (42C15) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Sampling theory in information and communication theory (94A20) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (3)

Universal sampling and interpolation in locally compact abelian groups ⋮ On sampling and interpolation by model sets ⋮ Uniqueness theory for model sets, and spectral superresolution

Cites Work

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• Quasicrystals, almost periodic patterns, mean-periodic functions and irregular sampling
• Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
• Landau's necessary density conditions for LCA groups
• Universal sampling and interpolation of band-limited signals
• The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
• On the Schwartz-Bruhat space and the Paley-Wiener theorem for locally compact Abelian groups
• Dirac combs
• Meyer's concept of quasicrystal and quasiregular sets
• Quasicrystals and Poisson's summation formula
• Quasicrystals are sets of stable sampling
• Multi-tiling and Riesz bases
• Universal sampling of band-limited signals
• Necessary density conditions for sampling an interpolation of certain entire functions
• Existence of Borel transversals in groups
• Sur certains groupes d'opérateurs unitaires
• Adeles et séries trigonométriques speciales
• Zeros of the Zak transform on locally compact abelian groups
• Simple quasicrystals are sets of stable sampling
• Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes $p$-adiques
• On the Linear Independence of Fractional Powers of Integers
• Principles of harmonic analysis
• Fourier pairs of discrete support with little structure

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