Universal spectra in \(G\times\mathbb{Z}_p\)

DOI10.1007/S00041-024-10074-2MaRDI QIDQ6550708

Wei-Qi Zhou

Publication date: 5 June 2024

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

zbMATH Keywords

spectral setsFuglede's conjectureuniversal spectrumtiling sets

Mathematics Subject Classification ID

Abstract finite groups (20D99) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Spectral synthesis on groups, semigroups, etc. (43A45)

Cites Work

• Periodicity of the spectrum in dimension one
• 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
• Rigidity of planar tilings
• Tiling the integers with translates of one finite set
• Spectral sets and factorizations of finite abelian groups
• 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
• Structure of tilings of the line by a function
• Fuglede's conjecture holds for cyclic groups of order \(pqrs\)
• Spectral sets and tiles in \(\mathbb{Z}_p^2 \times \mathbb{Z}_q^2\)
• The Fuglede conjecture for convex domains is true in all dimensions
• A type of factorization of finite Abelian groups
• THE SPECTRAL SET CONJECTURE AND MULTIPLICATIVE PROPERTIES OF ROOTS OF POLYNOMIALS
• Equi‐distributed property and spectral set conjecture on Zp2×Zp
• Combinatorial and harmonic-analytic methods for integer tilings
• Convex bodies which tile space by translation
• Replacement of Factors By Subgroups in the Factorization of Abelian Groups
• Rédei-matrices and applications
• The structure of translational tilings in $\mathbb{Z}^d$
• On the structure of spectral and tiling subsets of cyclic groups
• 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
• Fuglede’s conjecture fails in dimension 4
• Tiles with no spectra
• Universal spectra and Tijdeman's conjecture on factorization of cyclic groups
• Fuglede’s Conjecture Holds in \(\boldsymbol{\mathbb{Z}_{p}\times \mathbb{Z}_{p^{n}}}\)

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