On generalized weaving frames in Hilbert spaces (Q1638057)

Weaving frames have several applications in wireless sensor networks and the preprocessing of signals using Gabor frames. The concept of generalized frames or g-frames has been introduced by \textit{W. Sun} [J. Math. Anal. Appl. 322, No. 1, 437--452 (2006; Zbl 1129.42017)]. In the paper under review, necessary and sufficient conditions for weaving generalized frames and Riesz bases in Hilbert spaces are obtained. Some results discussed in [\textit{T. Bemrose} et al., Oper. Matrices 10, No. 4, 1093--1116 (2016; Zbl 1358.42025); \textit{P. G. Casazza} and \textit{R. G. Lynch}, ``Weaving properties of Hilbert space frames'', in: Proceedings of the 2015 international conference on sampling theory and applications, SampTA. Los Alamitos, CA: IEEE Computer Society. 110--114 (2015; \url{doi:10.1109/SAMPTA.2015.7148861})]) are extended to generalized weaving frames. Paley-Wiener type perturbation results also are studied for these frames.