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Weaving K-fusion frames in hilbert spaces
1. | School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China |
2. | School of Science, Dalian Minzu University, Dalian, 116600, China |
3. | School of Mathematics Science, Dalian University of Technology, Dalian, 116024, China |
$ K $-fusion frames are generalizations of fusion frames in frame theory. In this paper, based on the weaving frames and $ K $-fusion frames, we propose the notion of weaving $ K $-fusion frames and conduct relevant research. First, we give some characterizations of weaving $ K $-fusion frames. Then, by means of operator theory and frame theory, we present several novel construction approaches of weaving $ K $-fusion frames. Finally, we discuss transitivity of weaving $ K $-fusion frames.
References:
[1] |
T. Bemrose, P. G. Casazza, K. Gröchenig, M. C. Lammers and R. G. Lynch,
Weaving frames, Oper. Matrices, 10 (2016), 1093-1116.
doi: 10.7153/oam-10-61. |
[2] |
P. G. Casazza,
The art of frame theory, Taiwanese J. Math., 4 (2000), 129-202.
doi: 10.11650/twjm/1500407227. |
[3] |
P. G. Casazza, G. Kutyniok and S. Li,
Fusion frames and distributed processing, Appl. Comput. Harmon. Anal., 25 (2008), 114-132.
doi: 10.1016/j.acha.2007.10.001. |
[4] |
P. G. Casazza and G. Kutyniok,
Frames of subspaces, Wavelets, Frames and Operator Theory, 345 (2004), 87-113.
doi: 10.1090/conm/345/06242. |
[5] |
O. Christensen, An Introduction to Frames and Riesz Bases, 2$^nd$ edition, Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, [Cham], 2016.
doi: 10.1007/978-3-319-25613-9. |
[6] |
I. Daubechies, A. Grossmann and Y. Meyer,
Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), 1271-1283.
doi: 10.1063/1.527388. |
[7] |
S. G. Deepshikha, L. K. Vashisht and G. Verma, On weaving fusion frames for Hilbert spaces, 2017 International Conference on Sampling Theory and Applications (SampTA), Tallin, (2017), 381–385.
doi: 10.1109/SAMPTA.2017.8024363. |
[8] |
V. Deepshikha and L. K. Vashisht, Weaving $K$-frames in Hilbert spaces, Results. Math., 73 (2018), 20 pp.
doi: 10.1007/s00025-018-0843-4. |
[9] |
R. J. Duffin and A. C. Schaeffer,
A class of nonharmonic fourier series, Trans. Amer. Math. Soc., 72 (1952), 341-366.
doi: 10.1090/S0002-9947-1952-0047179-6. |
[10] |
P. A. Fillmore and J. P. Williams,
On operator ranges, Advances in Math., 7 (1971), 254-281.
doi: 10.1016/S0001-8708(71)80006-3. |
[11] |
D. Hua and Y. Huang,
Controlled $K$-g-frames in Hilbert spaces, Results Math., 72 (2017), 1227-1238.
doi: 10.1007/s00025-016-0613-0. |
[12] |
Y. Huang and S. Shi, New Constructions of $K$-g-frames, Results Math., 73 (2018), 13 pp.
doi: 10.1007/s00025-018-0924-4. |
[13] |
A. Khosravi and B. Khosravi,
Fusion frames and $g$-frames in Hilbert $C^{\ast}$-modules, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2008), 433-446.
doi: 10.1142/S0219691308002458. |
[14] |
A. Khosravi and K. Musazadeh,
Fusion frames and $g$-frames, J. Math. Anal. Appl., 342 (2008), 1068-1083.
doi: 10.1016/j.jmaa.2008.01.002. |
[15] |
D. Li and J. Leng, Fusion frames for operators and atomic systems, preprint, arXiv: 1801.02785. |
[16] |
F. A. Neyshaburi and A. A. Arefijamaal, Characterization and construction of $K$-fusion frames and their duals in hilbert spaces, Results Math., 73 (2018), 26 pp.
doi: 10.1007/s00025-018-0781-1. |
[17] |
F. A. Neyshaburi and A. A. Arefijamaal, Weaving Hilbert space fusion frames, preprint, arXiv: 1802.03352. |
[18] |
A. Rahimi, Z. Samadzadeh and B. Daraby, Woven fusion frames in Hilbert spaces, preprint, arXiv: 1808.03765. |
[19] |
S. Shi and Y. Huang, $K$-g-frames and their dual, Int. J. Wavelets Multiresolut. Inf. Process., 17 (2019), 11 pp.
doi: 10.1142/S0219691319500152. |
[20] |
W. Sun,
$G$-frames and $g$-Riesz bases, J. Math. Anal. Appl., 322 (2006), 437-452.
doi: 10.1016/j.jmaa.2005.09.039. |
show all references
References:
[1] |
T. Bemrose, P. G. Casazza, K. Gröchenig, M. C. Lammers and R. G. Lynch,
Weaving frames, Oper. Matrices, 10 (2016), 1093-1116.
doi: 10.7153/oam-10-61. |
[2] |
P. G. Casazza,
The art of frame theory, Taiwanese J. Math., 4 (2000), 129-202.
doi: 10.11650/twjm/1500407227. |
[3] |
P. G. Casazza, G. Kutyniok and S. Li,
Fusion frames and distributed processing, Appl. Comput. Harmon. Anal., 25 (2008), 114-132.
doi: 10.1016/j.acha.2007.10.001. |
[4] |
P. G. Casazza and G. Kutyniok,
Frames of subspaces, Wavelets, Frames and Operator Theory, 345 (2004), 87-113.
doi: 10.1090/conm/345/06242. |
[5] |
O. Christensen, An Introduction to Frames and Riesz Bases, 2$^nd$ edition, Applied and Numerical Harmonic Analysis, Birkhäuser/Springer, [Cham], 2016.
doi: 10.1007/978-3-319-25613-9. |
[6] |
I. Daubechies, A. Grossmann and Y. Meyer,
Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), 1271-1283.
doi: 10.1063/1.527388. |
[7] |
S. G. Deepshikha, L. K. Vashisht and G. Verma, On weaving fusion frames for Hilbert spaces, 2017 International Conference on Sampling Theory and Applications (SampTA), Tallin, (2017), 381–385.
doi: 10.1109/SAMPTA.2017.8024363. |
[8] |
V. Deepshikha and L. K. Vashisht, Weaving $K$-frames in Hilbert spaces, Results. Math., 73 (2018), 20 pp.
doi: 10.1007/s00025-018-0843-4. |
[9] |
R. J. Duffin and A. C. Schaeffer,
A class of nonharmonic fourier series, Trans. Amer. Math. Soc., 72 (1952), 341-366.
doi: 10.1090/S0002-9947-1952-0047179-6. |
[10] |
P. A. Fillmore and J. P. Williams,
On operator ranges, Advances in Math., 7 (1971), 254-281.
doi: 10.1016/S0001-8708(71)80006-3. |
[11] |
D. Hua and Y. Huang,
Controlled $K$-g-frames in Hilbert spaces, Results Math., 72 (2017), 1227-1238.
doi: 10.1007/s00025-016-0613-0. |
[12] |
Y. Huang and S. Shi, New Constructions of $K$-g-frames, Results Math., 73 (2018), 13 pp.
doi: 10.1007/s00025-018-0924-4. |
[13] |
A. Khosravi and B. Khosravi,
Fusion frames and $g$-frames in Hilbert $C^{\ast}$-modules, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2008), 433-446.
doi: 10.1142/S0219691308002458. |
[14] |
A. Khosravi and K. Musazadeh,
Fusion frames and $g$-frames, J. Math. Anal. Appl., 342 (2008), 1068-1083.
doi: 10.1016/j.jmaa.2008.01.002. |
[15] |
D. Li and J. Leng, Fusion frames for operators and atomic systems, preprint, arXiv: 1801.02785. |
[16] |
F. A. Neyshaburi and A. A. Arefijamaal, Characterization and construction of $K$-fusion frames and their duals in hilbert spaces, Results Math., 73 (2018), 26 pp.
doi: 10.1007/s00025-018-0781-1. |
[17] |
F. A. Neyshaburi and A. A. Arefijamaal, Weaving Hilbert space fusion frames, preprint, arXiv: 1802.03352. |
[18] |
A. Rahimi, Z. Samadzadeh and B. Daraby, Woven fusion frames in Hilbert spaces, preprint, arXiv: 1808.03765. |
[19] |
S. Shi and Y. Huang, $K$-g-frames and their dual, Int. J. Wavelets Multiresolut. Inf. Process., 17 (2019), 11 pp.
doi: 10.1142/S0219691319500152. |
[20] |
W. Sun,
$G$-frames and $g$-Riesz bases, J. Math. Anal. Appl., 322 (2006), 437-452.
doi: 10.1016/j.jmaa.2005.09.039. |
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