Fuglede's conjecture is false in 5 and higher dimensions

@inproceedings{Tao2003FugledesCI,
  title={Fuglede's conjecture is false in 5 and higher dimensions},
  author={Terence Tao},
  year={2003}
}
  • Terence Tao
  • Published 2003
  • Mathematics
  • We give an example of a set Ω ⊂ R 5 which is a finite union of unit cubes, such that L 2 (Ω) admits an orthonormal basis of exponentials { 1 |Ω|1/2 e 2πiξj ·x : 

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    Addendum to "Fuglede's conjecture fails in 4 dimensions over odd prime fields"

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    C A ] 2 0 D ec 2 01 9 Fuglede ’ s conjecture holds on Z 2 p × Z q

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    Fuglede's conjecture holds on $\mathbb{Z}_p^2 \times \mathbb{Z}_q$

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    Fuglede’s conjecture holds on cyclic groups Zpqr

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    Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$

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    On the discrete Fuglede and Pompeiu problems

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