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arXiv · 1709.05154

On weaving g-frames for Hilbert spaces

Dongwei Li·Jinsong Leng·Tingzhu Huang·Xiaoping Li
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Abstract

Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two necessary conditions in terms of frame bounds for weaving g-frames. Then we study the properties of weakly woven g-frames and give a sufficient condition for weaving g-frames. It is shown that weakly woven is equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz bases is considered. Finally, we present Paley-Wiener-type perturbation results for weaving g-frames.

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Dongwei Li, Jinsong Leng, Tingzhu Huang, Xiaoping Li. 2017-09-15. On weaving g-frames for Hilbert spaces. https://arxiv.org/abs/1709.05154

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