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February 2021 Weaving Hilbert space fusion frames
Fahimeh Arabyani-Neyshaburi, Ali Akbar Arefijamaal
Rocky Mountain J. Math. 51(1): 55-66 (February 2021). DOI: 10.1216/rmj.2021.51.55

Abstract

Weaving frame theory was recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, applied in many areas especially in wireless sensor networks. In this paper, we survey the notion of weaving Hilbert space fusion frames. This concept has potential applications in wireless sensor networks which require distributed processing using different fusion frames. Indeed, we present several approaches for identifying and constructing weaving fusion frames in terms of local frames, bounded operators in Hilbert spaces and also dual fusion frames. To this end, we present some conditions under which a fusion frame with its duals constitute pairs of woven fusion frames. As a result, we show that fusion Riesz bases are woven with all of their duals. Finally, we obtain some new results on fusion frames and weaving fusion frames under operator perturbations.

Citation

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Fahimeh Arabyani-Neyshaburi. Ali Akbar Arefijamaal. "Weaving Hilbert space fusion frames." Rocky Mountain J. Math. 51 (1) 55 - 66, February 2021. https://doi.org/10.1216/rmj.2021.51.55

Information

Received: 28 November 2018; Revised: 14 September 2019; Accepted: 30 September 2019; Published: February 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/rmj.2021.51.55

Subjects:
Primary: 42C15
Secondary: 43A35

Keywords: fusion frames , fusion Riesz bases , Hilbert space frames , woven fusion frames

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 1 • February 2021
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