Fuglede’s Conjecture for a Union of Two Intervals

@inproceedings{Laba2001FugledesCF,
  title={Fuglede’s Conjecture for a Union of Two Intervals},
  author={Izabella Laba},
  year={2001}
}
We prove that a union of two intervals in R is a spectral set if and only if it tiles R by translations. 1. The results A Borel set Ω ⊂ R of positive measure is said to tile R by translations if there is a discrete set T ⊂ R such that, up to sets of measure 0, the sets Ω + t, t ∈ T, are disjoint and ⋃ t∈T (Ω + t) = R . We may rescale Ω so that |Ω| = 1. We say that Λ = {λk : k ∈ Z} ⊂ R is a spectrum for Ω if {ek}k∈Z is an orthonormal basis for L(Ω). (1.1) A spectral set is a domain Ω ⊂ R such… CONTINUE READING
Highly Cited
This paper has 20 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-10 of 15 references

Fourier bases and a distance problem of Erdös, Math

  • A. Iosevich, N. H. Katz, S. Pedersen
  • Res. Lett
  • 1999

Spectral sets whose spectrum is a lattice with a base

  • S. Pedersen
  • J. Funct. Anal
  • 1996

Decomposition of the integers as a direct sum of two subsets

  • R. Tijdeman
  • London Math. Soc. Lecture Note Ser.,
  • 1995

Similar Papers

Loading similar papers…