Manufacturing pairs of woven frames applying duality principle on Hilbert spaces. (English) Zbl 1457.42041
Summary: Weaving Hilbert space frames have been introduced recently by T. Bemrose et al. [Oper. Matrices 10, No. 4, 1093–1116 (2016; Zbl 1358.42025)] to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle. In this regard, not only we obtain new properties in weaving frame theory related to dual frames but also we bring up new approaches for manufacturing pairs of woven frames. Specifically, we give some sufficient conditions under which a frame with its canonical dual, alternate duals or approximate duals constitute some concrete pairs of woven frames. Moreover, we provide some approaches for constructing weaving frames by using small perturbations and present a condition where different operators preserve the weaving property. As a consequence, the canonical duals of two woven frames are woven.
MSC:
| 42C15 | General harmonic expansions, frames |
Citations:
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