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Continuous weaving fusion frames in Hilbert spaces. (English) Zbl 1487.42076

Continuous frames in Hilbert spaces were introduced by S. T. Ali et al. [Ann. Phys. 222, No. 1, 1–37 (1993; Zbl 0782.47019)] and G. Kaiser [A friendly guide to wavelets. Boston: Birkhäuser (1994; Zbl 0839.42011)] independently. The notion of woven frames for a Hilbert space is given in [T. Bemrose et al., Oper. Matrices 10, No. 4, 1093–1116 (2016; Zbl 1358.42025)].
In this paper, the authors introduce the notion of weaving continuous fusion frames in separable Hilbert spaces. They obtain some results on preserving of the weaving continuous fusion frames and necessary and sufficient condition on weaving continuous fusion frames in section 2. In section 3, the paper continued studying of perturbation for weaving continuous fusion frames.

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)
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