پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 641 |
| تعداد مقالات | 9,370 |
| تعداد مشاهده مقاله | 68,046,024 |
| تعداد دریافت فایل اصل مقاله | 30,669,380 |
Discrete wave packets on non-Archimedean fields | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 11، دوره 16، شماره 9، آذر 2025، صفحه 117-126 اصل مقاله (450.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.23685.2581 | ||
| نویسندگان | ||
| Ishtaq Ahmed* ؛ Owais Ahmad؛ Neyaz Ahmad | ||
| Department of Mathematics, National Institute of Technology, Srinagar-190006, India | ||
| تاریخ دریافت: 24 خرداد 1400، تاریخ بازنگری: 27 تیر 1400، تاریخ پذیرش: 27 اسفند 1400 | ||
| چکیده | ||
| In this paper, we introduce a comprehensive theory of discrete wave packet systems on non-Archemedean fields by exploiting the machinery of Fourier transforms. We also define discrete periodic wave packet transform. A characterization of the system to be a Parseval frame and discrete periodic wave packet frame for $\ell^2(\mathcal Z)$ are obtained. | ||
| کلیدواژه‌ها | ||
| Wave packet frame؛ Non-Archimedean field؛ Discrete Fourier transform؛ Parseval frame | ||
| مراجع | ||
|
[1] I. Ahmed and N.A. Sheikh, a-inner product on local fields of positive characteristic, J. Nonlinear Anal. Appl. 2 (2018), no. 2, 64–75. [2] I. Ahmed and N.A. Sheikh, Dualwavelet frames in Sobolev spaces on local fields of positive characteristic, Filomat 34 (2020), no. 6, 2091–2099. [3] I. Ahmed and N.A. Sheikh, Perturbation of wavelet frames on non-Archimedean fields, Int. J. Nonlinear Anal. Appl. 13 (2021), no. 1, 197–208. [4] O. Ahmad, F.A. Shah and N.A. Sheikh, Gabor frames on non-Archimedean fields, Int. J. Geom. Meth. Mod. Phys. 15 (2018), 17 pages. [5] O. Christensen, An Introduction to Frames and Riesz Bases, Springer, New York, 2003. [6] O. Christensen and A. Rahimi, Frame properties of wave packet systems in L2(Rd), Adv. Comp. Math. 29 (2008), 101–111. [7] O. Christensen, Frames, bases, and discrete Gabor/wavelet expansions, Bull. Amer. Math. Soc. 38 (2001), 273–291. [8] C.K. Chui and X. Shi, Orthonormal wavelets and tight frames with arbitrary real dilations, Appl. Comput. Harmon. Anal. 9 (2000), 243–264. [9] A. Cordoba and C. Fefferman, Wave packets and Fourier integral operators Comm, Partial Differ. Equ. 3 (1978), 979–1005. [10] I. Daubechies, Ten Lecture on Wavelets, SIAM, Philadelphia (PA), 1992. [11] I. Daubechies, A. Grossman, and Y. Meyer, Painless non-orthogonal expansions, J. Math. Phys. 27 (1986), 1271–1283. [12] X. Dou, J. Jia, and Y. Liu, Spline wavelets in ℓ2(Z), J. Math. Anal. Appl. 321 (2006), 59–74. [13] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366. [14] D. Gabor, Theory of communications. J. Inst. Elect. Engn. 93 (1946), 429–457. [15] B. Han, Properties of discrete framelet transforms, Math. Model. Nat. Phenom 81 (2013), 18–47. [16] V.K. Ibnatovich, Nonspreading wave packets in quantum mechanics, Fond. Phys. 8 (1978), 564–571. [17] M. Kaur, B. Arora, and M. Mian, Wave packet construction in three-dimensional quantum billiards: Visualizing the closed orbit, collapse and revival of wave packets in the cubical billiard, J. Phys. 86 (2016), 31–48. [18] D. Labate, G. Weiss, and E. Wilson, An approach to the study of wave packet systems, Contemp. Math. Wavelets Frames Oper. Theory 345 (2004), 215–235. [19] D. Lu and D. Li, Frame properties of generalized shift-invariant systems in discrete setting, Appl. Anal. 95 (2016), 2535–2552. [20] A.K. Pan, Understanding the spreading of a Gaussian wave packet using the Bohmian machinery, J. Phys. 74 (2010), 867–874. [21] A. Ron and Z.W. Shen, Generalized shift-invariant systems, Constr. Approx. 22 (2005), 1–45. [22] A. Ron and Z.W. Shen Affine systems in L2(Rd): The analysis of the analysis operator, J. Func. Anal. Appl. 148 (1997), 408–447. [23] F.A. Shah and O. Ahmad, Wave packet systems on local fields, J. Geom. Phys. 120 (2017), 5–18. [24] M.H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, NJ, 1975. [25] V.S. Vladimirov, I.V. Volovich, and E.I. Zelnov, p-Adic Analysis and Mathematical Physics, Series in Soviet and East European Mathematics, Vol. 10, World Scientific Publishers, Singapore-New Jersey-London-Hong Kong, 1994. [26] M. Xu, D. Lu, and Q. Fan, Construction of Jth-stage discrete periodic wave packet frames, Appl. Anal. 97 (2018), no. 11, 1846–1866. | ||
|
آمار تعداد مشاهده مقاله: 578 تعداد دریافت فایل اصل مقاله: 74 |
||