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Department of Pure Mathematics, Faculty of Mathematical sciences, Ferdowsi University of Mashhad, Iran
10.22034/kjm.2020.169670.1308
Abstract
In this paper, we show that fusion frames in the finite dimensional Hilbert space $H$ correspond to frames in the Hilbert $C^*$-module $\mathcal{B}\left(\mathbb{C}^n\right)$. Moreover, we show that every tight fusion frame and Reisz fusion basis in $\mathbb{C}^n$ correspond to a tight frame and Reisz basis in the Hilbert $C^*$-module $\mathcal{B}\left(\mathbb{C}^n\right)$ respectively. Then, we use this fact to characterize the dual of Reisz fusion basis. Finally, we introduce Gabor fusion frames as a new notion.
Kamyabi-Gol, R. A., & Mohammadpour, M. (2021). The correspondence of Fusion frames and frames In Hilbert $C^*$-modules and finite Gabor Fusion frames. Khayyam Journal of Mathematics, 7(2), 187-200. doi: 10.22034/kjm.2020.169670.1308
MLA
Rajab Ali Kamyabi-Gol; Mozhgan Mohammadpour. "The correspondence of Fusion frames and frames In Hilbert $C^*$-modules and finite Gabor Fusion frames". Khayyam Journal of Mathematics, 7, 2, 2021, 187-200. doi: 10.22034/kjm.2020.169670.1308
HARVARD
Kamyabi-Gol, R. A., Mohammadpour, M. (2021). 'The correspondence of Fusion frames and frames In Hilbert $C^*$-modules and finite Gabor Fusion frames', Khayyam Journal of Mathematics, 7(2), pp. 187-200. doi: 10.22034/kjm.2020.169670.1308
VANCOUVER
Kamyabi-Gol, R. A., Mohammadpour, M. The correspondence of Fusion frames and frames In Hilbert $C^*$-modules and finite Gabor Fusion frames. Khayyam Journal of Mathematics, 2021; 7(2): 187-200. doi: 10.22034/kjm.2020.169670.1308