Relay fusion frames for Hilbert spaces

• Main Authors: Guoqing Hong, Pengtong Li
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Journal of Inequalities and Applications
• Subjects: Frame; Fusion frame; Relay fusion frame; Dual frame; Stability
• Online Access: http://link.springer.com/article/10.1186/s13660-019-2181-9

Abstract A new notion of frames, called the relay fusion frames, for Hilbert spaces has been introduced by the authors. It provides a mathematical framework for applications that require the transmission of signals over long distances or need to expand the coverage of wireless networks. The technique described in this paper is not only a natural technique suitable for the applications of relay communication systems, but also can be regarded as a natural generalization of fusion frames or even g-frames. We transfer some common properties in general frames and fusion frames to relay fusion frames with the definition of the relay fusion frames and their operators. In particular, besides canonical duality, we obtain two new dualities of the relay fusion frames. Moreover, we prove that relay fusion frames are stable under small perturbations.