On the rationality of the spectrum

DOI10.1007/s00041-017-9552-8zbMath1408.42022arXiv1606.04814OpenAlexW2963271040MaRDI QIDQ667662

Debashish Bose, Shobha Madan

Publication date: 1 March 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.04814

zbMATH Keywords

spectrumrationalityrecurrence sequencesspectral setszeros of exponential polynomialsFuglede's conjecture

Mathematics Subject Classification ID

Recurrences (11B37) General harmonic expansions, frames (42C15) Exponential Diophantine equations (11D61) Harmonic analysis in one variable (42A99)

Related Items (1)

On rationality of spectrums for spectral sets in \(\mathbb{R} \)

Cites Work

• Spectral sets and tiles on vector space over local fields
• Periodicity of the spectrum in dimension one
• The Fuglede conjecture holds in \(\mathbb{Z}_p\times \mathbb{Z}_p\)
• Spectrum is periodic for \(n\)-intervals
• The Fuglede spectral conjecture holds for convex planar domains
• Commuting self-adjoint partial differential operators and a group theoretic problem
• Fuglede's conjecture is false in 5 and higher dimensions
• Tiling the line with translates of one tile
• Fuglede's conjecture holds in \(\mathbb{Q}_p\)
• Fuglede's spectral set conjecture for convex polytopes
• A note on recurring series
• Fuglede’s conjecture for a union of two intervals
• On Fuglede's conjecture for three intervals
• THE SPECTRAL SET CONJECTURE AND MULTIPLICATIVE PROPERTIES OF ROOTS OF POLYNOMIALS
• “Spectral implies Tiling” for three intervals revisited
• On sets of integers containing k elements in arithmetic progression
• Fuglede's conjecture on cyclic groups of order pnq
• Some reductions of the spectral set conjecture to integers
• Fuglede’s conjecture fails in dimension 4
• Tiles with no spectra
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