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Multi-wavelet Bessel sequences in Sobolev spaces in $L^2(\mathbb{K})$ | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 14، دوره 13، شماره 2، مهر 2022، صفحه 141-149 اصل مقاله (400.43 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22970.2443 | ||
| نویسندگان | ||
| Ishtaq Ahmed* 1؛ Owais Ahmad2؛ Neyaz Ahmad2 | ||
| 1Department of Mathematics, Jammu and Kashmir Institute of Mathematical Sciences, Srinagar-190008, India | ||
| 2Department of Mathematics, National Institute of Technology, Srinagar-190006, India | ||
| تاریخ دریافت: 03 فروردین 1400، تاریخ بازنگری: 08 خرداد 1400، تاریخ پذیرش: 22 خرداد 1400 | ||
| چکیده | ||
| This paper is devoted to the study of some properties of multiwavelet Bessel sequences in Sobolev spaces over local fields of positive characteristics. | ||
| کلیدواژهها | ||
| Fourier transform؛ Bessel Sequence؛ Sobolev Space | ||
| مراجع | ||
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[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] O. Ahmad and N.A. Sheikh, Nonuniform wavelet frames on local fields, Jordan J. Math. Statist, 11 (2018), no. 1, 51–67. [3] I. Ahmed and N.A. Sheikh, Dual wavelet frames in Sobolev spaces on local fields of positive characteristic, Filomat 34 (2020), no. 6, 2091–2099. [4] O. Ahmad, N.A. Sheikh and M.A. Ali, Nonuniform nonhomogeneous dual wavelet frames in Sobolev spaces in L2(K), Afrika Math. 31 (2020), no. 7, 1145–1156. [5] J.J. Benedetto and R.L. Benedetto, A wavelet theory for local fields and related groups, J. Geom. Anal. 14 (2004), 423–456. [6] L. Dayong and L. Dengfeng, A characterization of orthonormal wavelet families in Sobolev spaces, Acta Math. Sci. 31 (2011), no. 4, 1475–1488. [7] B. Han and Q. Mo, Multiwavelet frames from refinable function vectors, Adv. Comput. Math. 18 (2003), no. 2, 211–245. [8] B. Han and Z. Shen, Dual wavelet frames and Riesz bases in Sobolev spaces, Constr. Approx. 29 (2009), no. 3, 369–406. [9] B. Han and Z. Shen, Characterization of Sobolev spaces of arbitrary smoothness using nonstationary tight wavelet frames, Isr. J. Math. 172 (2009), no. 1, 371–398. [10] Y. Li, S. Yang and D. Yuan, Bessel multiwavelet sequences and dual multiframelets in Sobolev spaces, Adv. Comput. Math. 38 (2013), no. 3, 491–529. [11] F.A. Shah and O. Ahmad, Wave packet systems on local fields, J. Geom. Phys. 120 (2017), 5–18. [12] F.A. Shah, O. Ahmad and A. Rahimi, Frames associated with shift invariant spaces on local fields, Filomat 32 (2018), no. 9, 3097–3110. [13] F.A. Shah, O. Ahmad and N.A. Sheikh, Orthogonal Gabor systems on local fields, Filomat 31 (2017), no. 16, 5193–5201. [14] F.A. Shah, O. Ahmad and N.A. Sheikh, Some new inequalities for wavelet frames on local fields, Anal. Theory Appl. 33 (2017), no. 2, 134–148. [15] M H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, NJ, 1975. [16] H. Zhang, Y. Dong and Q Fan, Wavelet frame based Poisson noise removal and image deblurring, Signal Process 137 (2017), 363–372. | ||
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