Co - affine systems in R d Brody Dylan
نویسندگان
چکیده
The proof of non-existence for co-affine frames is extended from the one-dimensional setting [GLWW] to the case of expansive dilation matrices in Rd. The problem of identifying subspaces on which co-affine systems may admit frame-type inequalities is then considered. In the context of multiresolution analysis it is shown that frame-type inequalities may hold on certain fundamental subspaces of an MRA. Finally, necessary conditions are given for a general co-affine system to admit frame-type inequalities on band-limited subspaces. In the case of the co-affine system generated by the Shannon wavelet these results dictate that Parseval’s identity holds on the band-limited subspace having bandwidth 2, but cannot hold with any larger bandwidth.
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