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...
