On the discrete Fuglede and Pompeiu problems

DOI10.2140/apde.2020.13.765OpenAlexW3105677912MaRDI QIDQ2174117

Gábor Somlai, Gergely Kiss, Máté Vizer, Romanos-Diogenes Malikiosis

Publication date: 17 April 2020

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.02844

zbMATH Keywords

tilingPompeiu problemspectral set conjecturevanishing sums of roots of unity

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Finite abelian groups (20K01) Functional equations for complex functions (39B32) Spectral synthesis on groups, semigroups, etc. (43A45)

Related Items

Spectral sets and tiles in \(\mathbb{Z}_p^2 \times \mathbb{Z}_q^2\), The two-sided Pompeiu problem for discrete groups, On the structure of spectral and tiling subsets of cyclic groups, On \(p\)-adic spectral measures, The null set of a polytope, and the Pompeiu property for polytopes, Fuglede’s Conjecture Holds in \(\boldsymbol{\mathbb{Z}_{p}\times \mathbb{Z}_{p^{n}}}\), The Coven-Meyerowitz tiling conditions for 3 odd prime factors, A counterexample to Fuglede's conjecture in \((\mathbb{Z}/p\mathbb{Z})^4\) for all odd primes, Equi‐distributed property and spectral set conjecture on Zp2×Zp, Combinatorial and harmonic-analytic methods for integer tilings, Fuglede's conjecture holds in \(\mathbb{Q}_p\), Fuglede's conjecture holds for cyclic groups of order \(pqrs\), Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}

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