Iterative reconstruction of continuous g-fusion frames in Hilbert spaces. (English) Zbl 1510.42043
In this article, the authors study continuous g-fusion frames in Hilbert spaces. The authors give some sufficient conditions for the existence of continuous g-fusion frames. Continuous g-fusion frames in finite-dimensional spaces are considered and a result is obtained.
Reviewer: Virender Dalal (Delhi)
MSC:
| 42C15 | General harmonic expansions, frames |
| 46C99 | Inner product spaces and their generalizations, Hilbert spaces |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
References:
| [1] | R. Ahmadi, Iterative reconstruction algorithm in frame of subspaces, Inter. J. Academic Research, 7(4) (2015), 157-161. |
| [2] | S. T. Ali, J. P. Antoine and J. P. Gazeau, Continuous frames in Hilbert spaces. Annals. of Physics, 222 (1993), 1-37. · Zbl 0782.47019 |
| [3] | B. G. Bodman, Optimal linear transmission by loss-insenstive packet en-coding, Appl. Comput. Harmon. 22 (2007), 274-285. · Zbl 1193.42113 |
| [4] | P. G. Casazza, and J. Kovacević, Equal-norm tight frames with erasures, Adv. Comput. Math. 18 (2003), 387-430. · Zbl 1035.42029 |
| [5] | P. G. Casazza, and G. Kutyniok, Frames of subspaces, Contemp. Math. 345 (2004), 87-114. |
| [6] | P. G. Casazza, and G. Kutyniok, Robustness of fusion frames under era-sures os subspaces and local frame vectors, Contemp. Math. 464 (2008), 149-160. · Zbl 1256.94017 |
| [7] | O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser, 2016. · Zbl 1348.42033 |
| [8] | M. H. Faroughi, and R. Ahmadi, Some properties of c-frames of subspaces, J. Nonlinear Sci. Appl. 1(3) (2008), 155-168. · Zbl 1171.42017 |
| [9] | M. H. Faroughi, A. Rahimi, and R. Ahmadi, GC-fusion frames, Methods Fanct. Anal. Top. 16 (2010), 112-119. · Zbl 1224.42084 |
| [10] | J. P. Gabardo and H. Deguang, Frames associated with measurable spaces, Adv. Compt. Math. 18 (2003), 127-147. · Zbl 1033.42036 |
| [11] | M. Khayyami, and A. Nazari, Construction of continuous g-frames and continuous fusion frames, Sahand Comm. Math. Anal. 4(1) (2016), 43-55. · Zbl 1413.42057 |
| [12] | G. Kutyniok, A. Pezeshki, A. R. Calderbank, and T. Liu, Robust dimen-sion reduction, fusion frames and Grassmannian packings, Appl. Compt. Harmon. Anal. 26 (2009), 64-76. · Zbl 1283.42046 |
| [13] | M. Rahmani, On some properties of c-frames, J. Math. Research with Appl. 37(4) (2017), 466-476. · Zbl 1399.42096 |
| [14] | V. Sadri, Gh. Rahimlou, R. Ahmadi, and R. Zarghami Farfar, Construction of g-fusion frames in Hilbert spaces, Inf. Dim. Anal. Quant. Prob. 23(2), 2050015, (2020), 1-18. · Zbl 1454.42029 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
