Holes in the Spectrum of Functions Generating Affine Systems
نویسندگان
چکیده
Given a d× d expansive dilation matrix D, a measurable set E ⊂ R d is called a Dt-dilation generator of Rd if Rd is tiled (modulo null sets) by the collection {(Dt)jE, j ∈ Z}. Our main goal in this paper is to prove certain results relating the support of the Fourier transform of functions generating a wavelet or orthonormal affine system associated with the dilation D to an arbitrary set E which is a Dt-dilation generator of Rd.
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