Some reductions of the spectral set conjecture to integers

DOI10.1017/S0305004113000558zbMath1294.52010arXiv1301.0814OpenAlexW3102943387WikidataQ122931404 ScholiaQ122931404MaRDI QIDQ5408754

Dorin Ervin Dutkay, Chun-Kit Lai

Publication date: 11 April 2014

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0814

zbMATH Keywords

spectral settilesFuglede conjectureCoven-Meyerowitz property

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Special sequences and polynomials (11B83) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (20)

Spectral sets and tiles in \(\mathbb{Z}_p^2 \times \mathbb{Z}_q^2\) ⋮ Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$ ⋮ Resonances for open quantum maps and a fractal uncertainty principle ⋮ A counterexample to Dutkay-Jorgensen conjecture ⋮ On the structure of spectral and tiling subsets of cyclic groups ⋮ On the discrete Fuglede and Pompeiu problems ⋮ The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set ⋮ Spectrality of self-similar tiles ⋮ On rationality of spectrums for spectral sets in \(\mathbb{R} \) ⋮ The Coven-Meyerowitz tiling conditions for 3 odd prime factors ⋮ Some Recent Developments of Self-Affine Tiles ⋮ Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution ⋮ On the rationality of the spectrum ⋮ Tight wavelet frame sets in finite vector spaces ⋮ On spectral sets of integers ⋮ Spectrality of certain self-affine measures on the generalized spatial Sierpinski gasket ⋮ Combinatorial and harmonic-analytic methods for integer tilings ⋮ Spectral theory of multiple intervals ⋮ Fuglede's conjecture holds for cyclic groups of order \(pqrs\) ⋮ Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}

Cites Work

• On Fuglede's conjecture and the existence of universal spectra
• Tiling the integers with translates of one finite set
• Spectral sets and factorizations of finite abelian groups
• Spectral sets whose spectrum is a lattice with a base
• 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
• A type of factorization of finite Abelian groups
• THE SPECTRAL SET CONJECTURE AND MULTIPLICATIVE PROPERTIES OF ROOTS OF POLYNOMIALS
• Universal spectra, universal tiling sets and the spectral set conjecture
• Fuglede’s conjecture fails in dimension 4
• Tiles with no spectra
• Universal spectra and Tijdeman's conjecture on factorization of cyclic groups

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