Spectral Sets and Factorizations of Finite Abelian Groups

  title={Spectral Sets and Factorizations of Finite Abelian Groups},
  author={J. Lagarias and Y. Wang},
  journal={Journal of Functional Analysis},
  • J. Lagarias, Y. Wang
  • Published 1997
  • Mathematics
  • Journal of Functional Analysis
  • Aspectral setis a subsetΩofRnwith Lebesgue measure 0<μ(Ω)<∞ such that there exists a setΛof exponential functions which form an orthogonal basis ofL2(Ω). The spectral set conjecture of B. Fuglede states that a set 0 is a spectral set if and only ifΩtilesRnby translation. We study setsΩwhich tileRnusing a rational periodic tile set S=Zn+A, where A⊆(1/N1) Z×…×(1/Nn) Zis finite. We characterize geometrically bounded measurable setsΩthat tileRnwith such a tile set. Certain tile sets S have the… CONTINUE READING
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