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Some Lie theory on Shearlet group | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 15، شماره 7، مهر 2024، صفحه 11-16 اصل مقاله (374.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29785.4261 | ||
| نویسندگان | ||
| Vahid Atayi* 1؛ Omid Pourbahry2 | ||
| 1Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2Department of Mathematics, Chalous Branch, Islamic Azad University, Chalous, Iran | ||
| تاریخ دریافت: 11 بهمن 1401، تاریخ بازنگری: 18 خرداد 1402، تاریخ پذیرش: 26 تیر 1402 | ||
| چکیده | ||
| In this work, using some tools of Lie theory, we compute the Lie algebra of the Shearlet group regarding as a 3-fold semidirect product Lie group. As we will see, it is a 3-fold semidirect sum of Lie algebras. | ||
| کلیدواژه‌ها | ||
| Shearlet group؛ Lie group؛ Lie algebra؛ exponential map؛ semidirect product | ||
| مراجع | ||
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[1] G.S. Alberti, F. De Mari, E. De Vito, and L. Mantovani, Reproducing subgroups of Sp(2;R). Part II: Admissible vectors, Monatsh. Math. 173 (2014), no. 3, 261–307. [2] G.S. Alberti, S. Dahlke, F. De Mari, E. De Vito, and H. F¨uhr, Recent progress in Shearlet theory: Systematic construction of Shearlet dilation groups characterization of wavefront sets and new embeddings in frames and other bases in abstract and function spaces ser. Appl. Numer. Harmon. Anal., Cham: Birkhauser/Springer, 2017, pp. 127-160. [3] V. Atayi and R.A. Kamyabi-Gol, On the characterization of subrepresentations of Shearlet group, Wavelets Linear Algebra 2 (2015), no. 1, 1–9. [4] S.H.H. Chowdhury and S.T. Ali, All the groups of signal analysis from the (1 + 1)-affine Galilei group, J. Math. Phys. 52 (2011), 103504. [5] S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark, and G. Teschke, The uncertainty principle associated with the continuous Shearlet transform, Int. J. Wavelets. Multiresolut. Inf. Process 6, (2008), 157–181. [6] S. Dahlke, F. Mari, E. Vito, S. Hauser, G. Steidl, and G. Teschke, Different faces of the Shearlet group, J. Geom. Anal. 26 (2016), no. 3, 1693–1729. [7] Grohs P., Continuous Shearlet tight frames, J. Fourier Anal. Appl., 17(3), (2011), 506-518. [8] K. Guo, D. Labate, and W.-Q. Lim, Edge analysis and identification using the continuous Shearlet transform, Appl. Comput. Harmon. Anal. 27 (2009), no. 1, 24–46. [9] K. Guo and D. Labate, Optimally sparse multidimensional representation using Shearlets, SIAM J. Math. Anal. 39, (2007), 298-318. [10] B.C. Hall, Lie groups, Lie algebras and representations, Springer, 2003. [11] J. Hilgert and K.H. Neeb, Structure and Geometry of Lie Groups, Springer, 2012. [12] R.A. Kamyabi-Gol V. Atayi, Abstract Shearlet transform, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 669-681. [13] G. Kutyniok and D. Labate, Shearlets, Birkhauser, 2012. [14] E. Nobari and S.M. Hosseini, A method for approximation of the exponential map in semidirect product of matrix Lie groups and some applications, J. Comput. Appl. Math. 234 (2010), 305–315. | ||
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