Spectral sets and tiles in \(\mathbb{Z}_p^2 \times \mathbb{Z}_q^2\)

DOI10.1016/j.jfa.2022.109472zbMath1506.43004arXiv2105.10575OpenAlexW4221115796MaRDI QIDQ2123118

Thomas Fallon, Gábor Somlai, Gergely Kiss

Publication date: 8 April 2022

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

Full work available at URL: https://arxiv.org/abs/2105.10575

zbMATH Keywords

finite geometryspectral settilingFuglede's conjecture

Mathematics Subject Classification ID

Finite abelian groups (20K01) Combinatorial aspects of finite geometries (05B25) Harmonic analysis on specific compact groups (43A75) Special aspects of infinite or finite groups (20F99) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Spectral synthesis on groups, semigroups, etc. (43A45)

Related Items

Tiling and spectrality for generalized Sierpinski self-affine sets ⋮ Fuglede’s Conjecture Holds in \(\boldsymbol{\mathbb{Z}_{p}\times \mathbb{Z}_{p^{n}}}\) ⋮ The Coven-Meyerowitz tiling conditions for 3 odd prime factors

Cites Work

• Unnamed Item
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• The Fuglede conjecture holds in \(\mathbb{Z}_p\times \mathbb{Z}_p\)
• Complex Hadamard matrices and the spectral set conjecture
• On Fuglede's conjecture and the existence of universal spectra
• Tesselation of integers
• Tiling the integers with translates of one finite set
• Fourier bases and a distance problem of Erdős
• 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
• On vanishing sums of roots of unity.
• A counterexample to Fuglede's conjecture in \((\mathbb{Z}/p\mathbb{Z})^4\) for all odd primes
• On the discrete Fuglede and Pompeiu problems
• Fuglede's conjecture fails in 4 dimensions over odd prime fields
• Tiling sets and spectral sets over finite fields
• Fuglede’s conjecture for a union of two intervals
• THE SPECTRAL SET CONJECTURE AND MULTIPLICATIVE PROPERTIES OF ROOTS OF POLYNOMIALS
• Equi‐distributed property and spectral set conjecture on Zp2×Zp
• Fuglede's conjecture on cyclic groups of order pnq
• Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}
• The structure of translational tilings in $\mathbb{Z}^d$
• Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$
• Periodicity and decidability of tilings of ℤ2
• Some reductions of the spectral set conjecture to integers
• Tiles with no spectra in dimension 4
• Fuglede’s conjecture fails in dimension 4
• Tiles with no spectra