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2018 On generalized weaving frames in Hilbert spaces
Lalit K. Vashisht, Saakshi Garg, Deepshikha, P.K. Das
Rocky Mountain J. Math. 48(2): 661-685 (2018). DOI: 10.1216/RMJ-2018-48-2-661

Abstract

Generalized frames (in short, $g$-frames) are a natural generalization of standard frames in separable Hilbert spaces. Motivated by the concept of weaving frames in separable Hilbert spaces by Bemrose, Casazza, Grochenig, Lammers and Lynch in the context of distributed signal processing, we study weaving properties of $g$-frames. Firstly, we present necessary and sufficient con\-ditions for weaving $g$-frames in Hilbert spaces. We extend some results of \cite Bemrose, Casazza, Grochenig, Lammers and Lynch, and Casazza and Lynch regarding conversion of standard weaving frames to $g$-weaving frames. Some Paley-Wiener type perturbation results for weaving $g$-frames are obtained. Finally, we give necessary and sufficient conditions for weaving $g$-Riesz bases.

Citation

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Lalit K. Vashisht. Saakshi Garg. Deepshikha. P.K. Das. "On generalized weaving frames in Hilbert spaces." Rocky Mountain J. Math. 48 (2) 661 - 685, 2018. https://doi.org/10.1216/RMJ-2018-48-2-661

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883485
MathSciNet: MR3810464
Digital Object Identifier: 10.1216/RMJ-2018-48-2-661

Subjects:
Primary: 42C15, 42C30, ‎42C40

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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