Geodesic
Weighted Riesz bases in g-fusion frames and their perturbation
Problemy analiza, Tome 9 (2020) no. 1, pp. 110-127.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce orthonormal and Riesz bases for g-fusion frames and show that the weights have basic roles. Next, we prove an effective theorem between frames and g-fusion frames by using an operator. Finally, perturbations of g-fusion frames will be presented.
Keywords: g-fusion frame, Dual g-fusion frame, gf-complete, gf-orthonormal basis, gf-Riesz basis. 
@article{PA_2020_9_1_a8,
     author = {G. Rahimlou and V. Sadri and R. Ahmadi},
     title = {Weighted {Riesz} bases in g-fusion frames and their perturbation},
     journal = {Problemy analiza},
     pages = {110--127},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2020_9_1_a8/}
}
TY  - JOUR
AU  - G. Rahimlou
AU  - V. Sadri
AU  - R. Ahmadi
TI  - Weighted Riesz bases in g-fusion frames and their perturbation
JO  - Problemy analiza
PY  - 2020
SP  - 110
EP  - 127
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2020_9_1_a8/
LA  - en
ID  - PA_2020_9_1_a8
ER  - 
%0 Journal Article
%A G. Rahimlou
%A V. Sadri
%A R. Ahmadi
%T Weighted Riesz bases in g-fusion frames and their perturbation
%J Problemy analiza
%D 2020
%P 110-127
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2020_9_1_a8/
%G en
%F PA_2020_9_1_a8
G. Rahimlou; V. Sadri; R. Ahmadi. Weighted Riesz bases in g-fusion frames and their perturbation. Problemy analiza, Tome 9 (2020) no. 1, pp. 110-127. http://geodesic.mathdoc.fr/item/PA_2020_9_1_a8/

[1] Blocsli H., Hlawatsch H. F., Fichtinger H. G., “Frame-theoretic analysis of oversampled filter bank”, IEEE Trans. Signal Processing. Anal., 46:12 (1998), 3256–3268 | DOI

[2] Candes E. J., Donoho D. L., “New tight frames of curvelets and optimal representation of objects with piecewise $C^2$ singularities”, Comm. Pure and App. Math. Anal., 57:2 (2004), 219–266 | DOI | MR | Zbl

[3] Casazza P. G., Christensen O., “Perturbation of operators and application to frame theory”, J. Fourier Anal. Appl. Anal., 3 (1997), 543–557 | DOI | MR | Zbl

[4] Casazza P. G., Kutyniok G., “Frames of subspaces”, Contemp. Math. Anal., 345 (2004), 87–114 | DOI | MR

[5] Casazza P. G., Kutyniok G., Li S., “Fusion frames and distributed processing”, Appl. Comput. Harmon. Anal., 25:1 (2008), 114–132 | DOI | MR | Zbl

[6] Christensen O., Frames and Riesz bases (An introduction course), Birkhäuser, 2008 | MR

[7] Diestel J., Sequences and series in Banach spaces, Springer-Verlag, New York, 1984 | MR

[8] Duffin R. J., Schaeffer A. C., “A class of nonharmonic Fourier series”, Trans. Amer. Math., 72:1, 341–366 | MR | Zbl

[9] Faroughi M. H., Ahmadi R., “Some properties of c-frames of subspaces”, J. Nonlinear Sci. Appl. Anal., 1:3 (2008), 155–168 | DOI | MR | Zbl

[10] Feichtinger H. G., Werther T., “Atomic systems for subspaces”, Proceedings SampTA (Orlando, FL, 2001), 163–165

[11] Găvruţa L., “Frames for operators”, Appl. Comp. Harm. Anal., 32 (2012), 139–144 | DOI | MR

[12] Heuser H., Functional analysis, John Wiley, New York, 1991 | MR

[13] Khayyami M., Nazari A., “Construction of continuous g-frames and continuous fusion frames”, SCMA. Anal., 4:1 (2016), 43–55 | Zbl

[14] Najati A., Faroughi M. H., Rahimi A., “G-frames and stability of g-frames in Hilbert spaces”, Method Func. Anal. Top., 14:3 (2008), 271–286 | MR | Zbl

[15] Sun W., “G-Frames and G-Riesz bases”, J. Math. Anal. Appl., 322 (2006), 437–452 | DOI | MR | Zbl