Oblique dual frames and shift-invariant spaces

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Banach Gelfand Triples for Gabor Analysis (2008, background): “In [6, 36], it is shown that any dual frame of {gk} can be written as”
Convex Optimization in Signal Processing and Communications (2009, background): “25) is satisfied if and only if [46] the supports IA and IS of φSS(e) and φAA(e) respectively coincide, and there exists a constant α > 0 such that |φSA(e)| > α, for all ω ∈ IA.”
Linear Independence of Finite Gabor Systems (2006, unknown): “Some papers on noncanonical duals or on minimizing with respect to other criteria than energy are [27], [ 30 ], [92].”
G-frames and G-Riesz Bases (2005, background): “2 Pseudo-frames (Li and Ogawa[17]), or similar, oblique frames(Christensen and Eldar [5, 10]) or outer frames (Aldroubi, Cabrelli, and Molter [1]) are studied recently in literature.”
Generalized Shift-Invariant Systems and Frames for Subspaces (2005, background): “For example, for a frame of translates, we proved in [3] that among the “classical duals” (i.”