assume ? ? l2(rd) has fourier transform continuous at the origin, with ˆ ?(0) = 1, and thatcan be represented by an affine series f = j>0 k?zd c j,k?j,k for some coefficients satisfying c 1(2) = j>0 k?zd |c j,k|2 1/2 <?. here ?j,k(x) = |deta j |1/2?(a jx ?k) and the dilation matrices a j expand, for example a j = 2j i. the result improves an observation by daubechies that t...