Affine frames, GMRA's, and the canonical dual
Tom 159 / 2003
Studia Mathematica 159 (2003), 453-479 MSC: Primary 42C40, 46N99. DOI: 10.4064/sm159-3-8
We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace $V_0$ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine frame has the quasi-affine structure.