Universal spectra, universal tiling sets and the spectral set conjecture

Authors

  • Steen Pedersen
  • Yang Wang

DOI:

https://doi.org/10.7146/math.scand.a-14325

Abstract

A subset Ω of Rd with finite positive Lebesgue measure is called a spectral set if there exists a subset ΛR such that EΛ:={ei2πλ,x:λΛ} 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 ΩR. 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.

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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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Articles