Orthonormal bases of exponentials for the n-cube

  title={Orthonormal bases of exponentials for the n-cube},
  author={J. C. Lagarias and J. Reeds and Y. Wang},
  journal={Duke Mathematical Journal},
  • J. C. Lagarias, J. Reeds, Y. Wang
  • Published 2000
  • Mathematics
  • Duke Mathematical Journal
  • Any set that gives such an orthogonal basis is called a spectrum for . Only very special sets in R are spectral sets. However, when a spectrum exists, it can be viewed as a generalization of Fourier series, because for the n-cube = [0,1]n the spectrum = Z gives the standard Fourier basis of L2([0,1]n). The main object of this paper is to relate the spectra of sets to tilings in Fourier space. We develop such a relation for a large class of sets and apply it to geometrically characterize all… CONTINUE READING
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