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The effect of perturbations of frames and fusion frames on their redundancies. (English) Zbl 1508.42038

Summary: An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships. Also, we express the redundancy of frames (fusion frames) in terms of the cosine angle between some subspaces.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
47A58 Linear operator approximation theory
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