The spectral set conjecture and multiplicative properties of roots of polynomials

By Izabella Laba. 2000

111 citations recorded by the source corpus.

Fuglede’s conjecture [2] states that a set Ω ⊂ R n tiles R by translations if and only if L 2 (Ω) has an orthogonal basis of exponentials. We obtain new partial results supporting the conjecture in dimension 1.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e53e959c8bdd766b8afbbaf655cb5152d1c52157

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Exponential spectra in L2(μ) (2013, methodology): “One of the interesting and basic questions in non-harmonic Fourier analysis is: What kind of compactly supported probability measures in Rd belong to the above classes of measures? When μ is the restriction of the Lebesgue measure on K with positive measure, the question whether it is a spectral mea”
Fuglede's conjecture on cyclic groups of order pnq (2016, methodology): “The direction Tile⇒Spectral can be deduced from the work of Coven-Meyerowitz [1] and Łaba [12] in the more general case when N has at most two prime divisors, and is shown in Section 3.”
Spectrality of Self-Similar Tiles (2013, background): “There are many partial results that involve a lot of techniques from harmonic analysis, operator theory, tiling theory, convexgeometry, andgeometryof numbers [19–21,27,28,33,39].”
Fuglede’s conjecture fails in dimension 4 (2005, background): “…will restrict our attention to sets of the form of a finite union of unit cubes placed at points with integer coordinates, i.e., (1) Ω = ⋃ t∈Γ {t + [0, 1)d}, where Γ ⊂ Zd is finite (this means, essentially, that we will be considering the tiling and spectral properties of sets in Zd).”