Spectrality and tiling by cylindric domains

DOI10.1016/j.jfa.2016.04.021zbMath1348.42023arXiv1602.08850OpenAlexW2291252532MaRDI QIDQ322375

Rachel Greenfeld, Nir Lev

Publication date: 7 October 2016

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

Full work available at URL: https://arxiv.org/abs/1602.08850

zbMATH Keywords

exponential functionstilingspectral setscomplete orthogonal systemcylindric domainsFuglede's conjecture

Mathematics Subject Classification ID

Harmonic analysis in several variables (42B99) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items (9)

Fuglede's spectral set conjecture for convex polytopes ⋮ Packing near the tiling density and exponential bases for product domains ⋮ Spectrality of product domains and Fuglede's conjecture for convex polytopes ⋮ Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets ⋮ Spectral sets and weak tiling ⋮ Tiling and spectrality for generalized Sierpinski self-affine sets ⋮ The structure of translational tilings in $\mathbb{Z}^d$ ⋮ Infinite orthogonal exponentials for a class of Moran measures ⋮ Unnamed Item

Cites Work

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• Spectral pairs in Cartesian coordinates
• The Fuglede spectral conjecture holds for convex planar domains
• Orthonormal bases of exponentials for the \(n\)-cube
• Fourier bases and a distance problem of Erdős
• Non-symmetric convex domains have no basis of exponentials
• Commuting self-adjoint partial differential operators and a group theoretic problem
• Fuglede's conjecture is false in 5 and higher dimensions
• Fuglede's spectral set conjecture for convex polytopes
• Convex bodies with a point of curvature do not have Fourier bases
• Convex bodies which tile space by translation
• Packing, Tiling, Orthogonality and Completeness
• Orthogonal exponentials on the ball

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