"Fusion Frame Multipliers"Köhldorfer, LukasFrame multipliers are operators, which act on a given signal via an analysis transform, followed by pointwise multiplication with a symbol, and re-synthesizing the information. They naturally appear in physics, in the diagonalization process of operators, and in a variety of applications such as signal processing and acoustics. In the last view years, the concept of frame multipliers has been extended to fusion frames, which generalize classical (Hilbert space) frames and entail many interesting problems, which disappear or are easier to solve in frame theory. We give a more general definition of a fusion frame multiplier than usually found in literature and justify, why we think that our definition is still the most canonical one. We present a number of results for fusion frame multipliers, that are also true in the classical frame case, but also point out some key differences to frame multipliers, coming from the subtle difficulties arising in fusion frame theory. |
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