Abstract
In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-frame and fusion frame. K-fusion frames come naturally, having significant applications, when one needs to reconstruct functions (signals) from a large data in the range of a bounded linear operator. Motivated by the concept of weaving frames, in this paper we study wovenness of K-fusion frames. This article presents characterizations of weaving K-fusion frames. Paley-Wiener type perturbations and conditions on erasure of frame components are discussed to examine wovenness.
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References
Bemrose, T., Casazza, P. G., Gröchenig, K., Lammers, M. C. and Lynch, R. G., Weaving frames, Oper. Matrices. 10 (4)(2016), 1093–1116.
Bhandari, A. and Mukherjee, S., Atomic subspaces for operators, Indian J. Pure Appl. Math. 51 (3)(2020), 1039–1152.
Bhandari, A., Mukherjee, S.: Characterizations of woven frames, Int. J. Wavelets Multiresolut. Inf. Process 18 (5)(2020), 2050033.
Casazza, P. G. and Lynch, R. G., Weaving properties of Hilbert space frames, International Conference on Sampling Theory and Applications (SampTA), (2015).
Christensen, O., Frames and Bases-An Introductory Course, Birkhäuser, Boston, 2008.
Daubechies, I., Grossmann, A. and Meyer, Y., Painless nonorthogonal expansions, J. Math. Phys. 27(5)(1986), 1271–1283.
Deepshikha and Vashisht, L. K., Weaving \(K\)- frames in Hilbert spaces, Results Math. 73:81(2018).
Duffin, R. and Schaeffer, A. C., A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72(2)(1952), 341–366.
Gǎvruţa, P., On the duality of fusion frame, J. Math. Anal. Appl. 333(2)(2007), 871–879.
Garg, S. and Vashisht, L. K., Weaving \(K\)- fusion frames in Hilbert spaces, Ganita 67(1)(2017), 41–52.
Kato, T., Perturbation Theory for Linear Operators, Springer, New York, 1980.
Li, X. B., Yang, S. Z. and Zhu, Y. C., Some results about operator perturbation of fusion frames in Hilbert spaces, J. Math. Anal. Appl. 421(2015), 1417–1427.
Liu, A. F. and Li, P. T., \(K\)-fusion frames and the corresponding generators for unitary systems, Acta Math. Sin. (Engl. Ser.) 34 (5)(2018), 843–854.
Neyshaburi, F. A. and Arefijamaal, A. A., Characterization and construction of \(K\)-fusion frames and their duals in Hilbert spaces, Results Math. 73:47 (2018).
Acknowledgements
The first author acknowledges the fiscal support of MHRD and the academic support of VIT Bhopal University, Government of India. The second author is supported by DST-SERB project MTR/2017/000797.
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Bhandari, A., Mukherjee, S. (2022). On Wovenness of K-Fusion Frames. In: Yilmaz, F., Queiruga-Dios, A., Santos Sánchez, M.J., Rasteiro, D., Gayoso Martínez, V., Martín Vaquero, J. (eds) Mathematical Methods for Engineering Applications. ICMASE 2021. Springer Proceedings in Mathematics & Statistics, vol 384. Springer, Cham. https://doi.org/10.1007/978-3-030-96401-6_8
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