Perturbation of wavelet frames on non-Archimedean fields

Document Type : Research Paper


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


The paper deals with two different aspects of wavelet frames. First, we obtain a necessary condition on irregular wavelet frames on local fields of positive characteristic and in the second aspect, we present some results on the perturbation of wavelet frames, when we disturb the mother function of a wavelet frame or dilation parameter. All the results have been carried without the compactness of support neither on generating function nor on its Fourier transform.


[1] J. J. Benedetto, R.L. Benedetto, A wavelet theory for local fields and related groups, J. Geom. Anal. 14 (2004) 423–456.
[2] O. Christensen, An Introduction to Frames and Riesz Bases, Springer, 2003.
[3] O. Christensen and A. Rahimi, Frame properties of wave packet systems in L2 (Rd), Adv. Comput. Math. 29 (2008) 101-111.
[4] F. Galindo and J. Sanz, Multiresolution analysis and Radon measures on a locally compact Abelian group, Czechoslovak Math. J., 51(4) (2001) 859–871.
[5] S.F. Lukomskii, Multiresolution analysis on product of zero-dimensional Abelian groups, J. Math. Anal. Appl. 385 (2012) 1162–1178.
[6] D. Ramakrishan and R.J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics, Springer, New York, 1999.
[7] F. A. Shah and Abdullah, A characterization of tight wavelet frames on local fields of positive characteristic, J. Contemp. Math. Anal. 49(6) (2014) 251–259.
[8] M.H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, 1975.
Volume 13, Issue 1
March 2022
Pages 197-208
  • Receive Date: 23 November 2020
  • Revise Date: 20 January 2021
  • Accept Date: 04 March 2021