Multi-wavelet Bessel sequences in Sobolev spaces in $L^2(\mathbb{K})$

Document Type : Research Paper

Authors

1 Department of Mathematics, Jammu and Kashmir Institute of Mathematical Sciences, Srinagar-190008, India

2 Department of Mathematics, National Institute of Technology, Srinagar-190006, India

Abstract

This paper is devoted to the study of some properties of multiwavelet Bessel sequences in Sobolev spaces over local fields of positive characteristics.

Keywords

[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.
Volume 13, Issue 2
July 2022
Pages 141-149
  • Receive Date: 23 March 2021
  • Revise Date: 29 May 2021
  • Accept Date: 12 June 2021