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Perturbations on K-fusion frames

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, for example, wireless sensor networks. In this paper, we discuss a generalization of fusion frames, K-fusion frames. K-fusion frames provide decompositions of a Hilbert space into atomic subspaces with respect to a bounded linear operator. This article studies various kinds of properties of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.
Słowa kluczowe
Wydawca
Rocznik
Strony
175--185
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
  • Department of Mathematics, NIT Meghalaya, Shillong-793003, India
  • Department of Mathematics, NIT Meghalaya, Shillong-793003, India
Bibliografia
  • [1] A. Arefijamaal and E. Zekaee, Image processing by alternate dual Gabor frames, Bull. Iranian Math. Soc. 42 (2016), no. 6, 1305-1314.
  • [2] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., Springer, New York, 2003.
  • [3] A. Bhandari and S. Mukherjee, Atomic subspaces for operators, Indian J. Pure Appl. Math. 51 (2020), no. 3, 1039-1052.
  • [4] P. G. Casazza and G. Kutyniok, Frames of subspaces, in: Wavelets, Frames and Operator Theory, Contemp. Math. 345, American Mathematical Society, Providence (2004), 87-113.
  • [5] P. G. Casazza and G. Kutyniok, Finite Frames. Theory and Applications, Appl. Numer. Harmon. Anal., Springer, New York, 2013.
  • [6] P. G. Casazza, G. Kutyniok and S. Li, Fusion frames and distributed processing, Appl. Comput. Harmon. Anal. 25 (2008), no. 1, 114-132.
  • [7] P. G. Casazza, G. Kutyniok, S. Li and C. J. Rozell, Modeling sensor networks with fusion frames, Proc. SPIE 6701 (2007), Article ID 67011M.
  • [8] O. Christensen, Frames and Bases. An Introductory Course, Appl. Numer. Harmon. Anal., Birkhäuser, Boston, 2008.
  • [9] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27 (1986), no. 5, 1271-1283.
  • [10] R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415.
  • [11] R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.
  • [12] P. Ferreira, Mathematics for multimedia signal processing II: Discrete finite frames and signal reconstruction, in: Signal Processing for Multimedia, IOS Press, Amsterdam (1999), 35-54.
  • [13] L. Găvruța, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012), no. 1, 139-144.
  • [14] P. Găvruța, On the duality of fusion frames, J. Math. Anal. Appl. 333 (2007), no. 2, 871-879.
  • [15] K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, New York, 2001.
  • [16] A. Gumber and N. K. Shukla, Uncertainty principle corresponding to an orthonormal wavelet system, Appl. Anal. 97 (2018), no. 3, 486-498.
  • [17] D. Han and D. R. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc. 147 (2000), no. 697, 1-94.
  • [18] Q. Huang, L. Zhu, W. Geng and J. Yu, Perturbation and expression for inner inverses in Banach spaces and its applications, Linear Algebra Appl. 436 (2012), no. 9, 3721-3735.
  • [19] D. Li and J. Leng, Fusion frames for operators and atomic systems, preprint (2018), https://arxiv.org/abs/1801.02785v1.
  • [20] X.-B. Li, S.-Z. Yang and Y.-C. Zhu, Some results about operator perturbation of fusion frames in Hilbert spaces, J. Math. Anal. Appl. 421 (2015), no. 2, 1417-1427.
  • [21] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (2006), no. 1, 437-452.
  • [22] G. Verma, L. K. Vashisht and M. Singh, On excess of retro Banach frames, J. Contemp. Math. Anal. 54 (2019), no. 3, 143-146.
  • [23] X.-C. Xiao, Y.-C. Zhu and M.-L. Ding, Erasures and equalities for fusion frames in Hilbert spaces, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 3, 1035-1045.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-721e0b7d-be2a-442d-9de7-ef55ff3ac4e2
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