Universal spectra, universal tiling sets and the spectral set conjecture
DOI:
https://doi.org/10.7146/math.scand.a-14325Abstract
A subset Ω of Rd with finite positive Lebesgue measure is called a spectral set if there exists a subset Λ⊂R such that EΛ:={ei2π⟨λ,x⟩:λ∈Λ} form an orthogonal basis of L2(Ω). The set Λ is called a spectrum of the set Ω. The Spectral Set Conjecture states that Ω is a spectral set if and only if Ω tiles Rd by translation. In this paper we prove the Spectral Set Conjecture for a class of sets Ω⊂R. Specifically we show that a spectral set possessing a spectrum that is a strongly periodic set must tile R by translates of a strongly periodic set depending only on the spectrum, and vice versa.Downloads
Published
2001-06-01
How to Cite
Pedersen, S., & Wang, Y. (2001). Universal spectra, universal tiling sets and the spectral set conjecture. MATHEMATICA SCANDINAVICA, 88(2), 246–256. https://doi.org/10.7146/math.scand.a-14325
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