Orthonormal Bases of Exponentials for the N-cube Orthonormal Bases of Exponentials for the N-cube
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چکیده
A compact domain in R n is a spectral set if there is some subset of R n such that fexp(2ih; xi) : 2 g when restricted to gives an orthogonal basis of L 2 ((). The set is called a spectrum for. We give a criterion for being a spectrum of a given set in terms of tiling Fourier space by translates of a suitable auxiliary set D. We apply this criterion to classify all spectra for the n-cube by showing that is a spectrum for the n-cube if and only if f + 0; 1] n : 2 g is a tiling of R n by translates of unit cubes.
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تاریخ انتشار 1998