Pseudo-Duals of Frames with Applications

By Shidong Li, H. Ogawa. 2001

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A Theory of Generalized Multiresolution Structure and Pseudoframes of Translates (2001, background): “� x, xn� x ∗ in H . See, e.g., [13, 14 ]. For more references on frames and relevant terminologies, we refer readers to, e.g., [1, 6, 7, 8, 9, 10, 11], and [23].”
Linear Independence of Finite Gabor Systems (2006, result): “Some papers on noncanonical duals or on minimizing with respect to other criteria than energy are [27], [30], [ 92 ].”
Oblique dual frames and shift-invariant spaces (2004, background): “The actual content of the lemma the idea of stating the lemma in this form comes from the paper [17].”
The uniqueness of the dual of Weyl-Heisenberg subspace frames (2004, background): “Besides this standard dual, a frame which is not a Riesz b can have many other duals (these other duals are also called pseudo-duals by Li [23,24] or altern by Han and Larson [18]).”